Develop Reference

What are the various ways of creating OpenGl ES graphics on Android?

I have done some reading on OpenGl ES for Android. I know that I could make a game with the canvas API, but I would like to experiment with OpenGl ES first.
From here I can see two options: Use a game engine or develop my OpenGl ES from the ground up.
The coder/math person that I am is pushing me to the harder option(second option). The way I want to start on this journey is by creating a mesh and manipulating it with various transformations. I will worry about the textures later on. I've learned that I could develop my mesh using outside software such as Blender or LibGdx. However, I would like to learn to develop it with the android API. Do you think this is possible? Will it be very taxing for the android system to process many meshes and transform them? I think It will.
Should I just stick to the game engine way, and forget the "from the ground up mindset".
I also just found out about the replica island source code. Perhaps, I should start reading it and tweaking it on my own.
One more thing, from what I see, I have several options when developing graphics on android using OpenGl ES. Create the 3D model meshes or use sprites(such as replica island). Are there any other ways of doing this?

It all depends on the complexity of the game.
If it's on the simpler side, you could very well 'start from scratch'. I'm pretty sure, you'll end up creating something similar to replica island. For a complex game, you'll be near (as we're from moon) unity on the other extreme. We're talking about hundreds of thousands of man-hours.
As far as creating the meshes is concerned, OpenGL(ES) can only render the meshes.
Unless it's a very primitive mesh or one which can be modelled mathematically with a few equations (less likely for a game), you'll have to create them in blender, maya etc.
For a first timer, I suggest reusing an existing game/engine.
The transition from rendering meshes, then applying textures, then using lighting and shadows etc has a decent learning curve.
Trust me, even with this approach the coder/Math person will have enough on his plate.

Will LibGDX supports 3D like Unity3D

Can anyone please tell me that will libgdx supports 3D like Unity3D and please tell me some games which are built on libgdx 3d if possible.

Your question is pretty general, but the libGDX 3D API is pretty stable, easy to use and has many features.
It can not only render basic 3D shapes like spheres and boxes, but also load complex models via .obj or .fbx files. It supports animations, normal and specular maps, a basic lighting system with point lights and directional lights. The latest version also added a high-performance 3D particle engine, including an editor to create those effects.
Furthermore it supports bullet physics which is a 3D physics engine which works pretty well with the 3D API of libGDX.
I'm currently developing a 3D game myself and I can only say that everything works really nicely. The performance is great and with my old laptop I can render several million textured tris with lighting at 60FPS. One example of an already published cross platform 3D game made with libGDX is Delver (its graphics are very simplistic though and do not show the capabilities of libGDX that well).

Canvas or OpenGL ES2 for Android 2D game?

OK, so I just got this idea for a game. I already know how to develop for Android, so I though of developing for Android first.
The game (without revealing too much :D) will have a single shape onscreen all the time. It will have to smoothly change shape, color etc. in response to a few knobs/sliders on the screen.
As we do not have multiple shapes/objects I do not need any form of physics engine now. I need to be able to draw polygons and transition colors/gradients effortlessly. I'm targeting a high FPS for this game (think PewPew/2Fuse!)
Do I need OpenGL for this? If so, where can I learn it?
(I'm aware that OpenGL is difficult, and that it's time-consuming to learn.)

I can only offer some of my views. Programming a game is much about transferring artistic assets from the programs, in which they are created (3D modeling programs, Photoshop, Gimp, ...), into your own program. Whether you select OpenGL or Canvas is therefore somewhat dependent upon the nature of your assets (3D models, or bitmaps only, for example). You should be aware however, that on modern Android devices OpenGL ES support is universal and that on those devices the Canvas is implemented with OpenGL ES. Choosing OpenGL ES therefore eliminates one level of indirection. You also have libraries like Cocos2D that offer 2D APIs, but use OpenGL for implementation. To conclude, without top-notch artistic assets your game cannot succeed, if those are good however, even a game using the Canvas may succeed.
EDIT: I think you should proceed like this:
game design -> assets implementing game design -> API offering the shortest path towards the reproduction of the assets in your game

If your assets are polygon based (as you mention in a comment) you should go with OpenGL ES 2.0. OpenGL ES 2.0 is non-trivial to learn, but in learning it, you would gain some marketable skills and experience, and you could make work that is very "showy" for a programmer. Just be patient and try to understand how it works and not just "slop through it."
A great place to start learning is with a tutorial like this one.

3D Engine with movie texture for iOS/Android?

Is there any high level 3D engine capable of displaying movie texture on both iOS and Android?
This would be for a project close to a virtual museum with video playing on some walls. The engine would also be able to import 3D model from 3DS Max.
I checked major 3D engines but did not find the ideal one. Unity3D for instance does not support movie texture.
I am wondering if I can avoid coding low level OpenGL code on each platform.

Unity does not support movie textures on mobile out of the box, but this Mobile Movie Texture plugin works quite well:
http://u3d.as/content/defiant-development-pty-ltd/mobile-movie-texture/2w1
p.s. I think it requires Unity Pro

Unity3D supports movie textures. Update: only for desktop, it seems.
An alternative that does appear to work is Bink from Rad Game Tools. This is just a (proprietary) video decoder library though that you'll most probably have to incorporate into your own engine (I believe I'm right in saying that you can specify the memory buffer the video is rendered to, so once you have the frame you can do whatever you like with it).

Android 2D game development without an engine

I want to know the best way or a tool for making a good Android game!, I mean by "good" that the game must have a nice performance no lags or something like that, ..
So I will begin by 2D game development, and I want to avoid "Game engines"! ..
So what's the best way?! - to make it by Open GL ES or there another way?! ..

You should be able to learn a lot about open gl graphics programming by looking at Replica Island. Its an open source 2d Platform game which uses no engine.
The author gave some talks on Google IO which might be of interest to you:
http://www.youtube.com/watch?v=U4Bk5rmIpic
http://www.youtube.com/watch?v=7-62tRHLcHk
http://www.youtube.com/watch?v=cdvaPyq_eBU

It's possible that this is considered too broad a question - we can't tell you how to make a game. But in response to your last question: yes, OpenGL is the best way to make a high performance game in 2D or 3D. If you have a more slow moving, turn based game, then you could stick to a Canvas on a SurfaceView or even use basic View widgets to build up the layout of a game board.
But if it's your first game, unless you have a lot of time and patience, I would strongly urge you to try an existing game engine. You may not realise how much work goes into a decent game engine until you're halfway (or 10% of the way) into making one. Have a look at the source of an engine like LibGDX and think about whether it's the sort of thing you'd be able to write.
There's plenty of info in the Android graphics dev guide.

You do not need a game engine to develop a 2D game in Android. You do not need to use SurfaceView either. SurfaceView, OpenGL and AndEngine and (maybe other game engines) have issues with consistent sprite animation speed and size of sprites across the various Android devices. Especially when the game has complex sprite movements. I went crazy trying to build a 2D game with consistent speed movement of sprites and sprite sizes in relation to screen size and density (e.g. tablets vs phones). So, I decided to drop the game engines and this is how I accomplished my first recently published 2D Android game:
Use drawable-nodpi for sprite images (gives sprite size consistency
across screen densities and sizes)
Use different layouts to support various screen sizes (e.g.
layout-large, layout-xlarge, etc...)
Use TranslateAnimation and ObjectAnimator to animate sprite movements across screen
Use math to figure out sprites collision (e.g. screen coordinates and sprite location etc.)
Use handlers and condition statements to control the game events
You can test the outcome of following the above guide to developing a 2D Android game without game engine by checking out the game. It is called Yum Yum Pow available on Google Play. The free limited version is available also on Google Play. I can only link to free apps I think, so here it is:
https://play.google.com/store/apps/details?id=com.wildroid.yum.yum.pow.limited

If u are planning to build a simple game then stick with Basic android.If it is a big game,With out game engine your game developing will be a heavier process.if u want to use a lot of images then memmory problem will occur(OOM).if u are comfort with the game engine that will be easy for future game developing.if u are making a simple game then there is no need of game engines.
there are so many game engines available
andengine,libgdx,cocos2d..