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I want to retrieve the latitude and longitude of a location shown in google map route between two locations

I have lat and long of some locations in JSON. I want to spot whether these locations are present in a route shown by google maps.

Here are the steps I'd consider to achieve the effect you want:
Query for a DirectionResponse https://developers.google.com/maps/documentation/directions/intro#DirectionsResponses
For each polyline of each step of each leg, test whether your locations are close to the line. For simplicity you can also use the overview_polyline. Unfortunately this is not simple to do out-of-the-box using the Maps API alone. Check this thread for inspiration on a manual implementation. Find a point in a polyline which is closest to a latlng
Alternatively, convert the polylines to GeoJSON, and process using a spatial library such as JSTS or Turf. E.g. the latter provides a pointOnLine function.

How to show two location on Google map which is enter by user and draw the route between them

I have two EditText where user enter two city name I want draw route between two city and distance between them on Google map.

You can use Google Directions API to get the routes between them.
https://maps.googleapis.com/maps/api/directions/json?origin=Boston,MA&destination=Concord,MA&waypoints=Charlestown,MA|Lexington,MA
Then you can see the accepted answer here of how to encode the "points"-parameter to LatLng's / Polylines.
This should cover your question i guess:
Get driving directions using Google Maps API v2
What you need to know to do this: How to do network requests, how to parse JSON, and how to setup a GoogleMap in your app.

Generating a map in android

if i'm given a set of points(latitude,longitude) how can i generate a map with them between the points such that route generated is optimum.
i have no clue about it and so I've not mentioned the code along with it.
my purpose is to extract the latitudes and longitudes of points from a table in my local database and then generate a map with it .

I would use the Google Directions API to determine routes between each of the geolocations. Here is an introduction to Google Directions. Part of the way down there is a, "Use Waypoints in Routes", which allow you to specify one or more addresses to determine a route.
If you need help getting started with Google Maps API, here's an introduction.

What you are looking for is, can be acheived by google maps api, using waypoint parameter
http://maps.googleapis.com/maps/api/directions/json?origin=Boston,MA&destination=Concord,MA&waypoints=Charlestown,MA|via:Lexington,MA&key=API_KEY
in waypoint, either you can supply the location name or geo coordinates which should be delimeted by | incase you have multiple points, please follow this link for more detail about its usage.
https://developers.google.com/maps/documentation/directions/#DirectionsRequests

Marking places in android app not on the 'Google Places' database

I want to add markers on map for my android app. I do know how to do it (overlay items). My question is: Since I am manually putting markers on points(on the map) whose lat/long's I already know, I want to know if there is any way to get the exact latitude and longitude of a place on google map? Right now I am asking my people to go to the particular places and use this ( http://bit.ly/K4fOcy ) app to determine the lat/long of that place and send it to me via e-mail. I use these lat/long values to put markers on my map in the app. But the latitudes and longitudes i get are not accurate. they have around 300-2500m error (on real scale).
Or shall I use the Google Places API? How does it work? What about the places which are not in the Google Places database? How do I exactly mark them on the map? I would be very grateful if someone points me in the right direction.
Thanks

If you are working with establishments that aren't represented in the Google Places API and want to be able to pull coordinates directly from http://maps.google.com/, you simply:
Find the location of interest on the map, using an address or just knowledge of the area
Right-click on the map and select What's here? from the context pop-up menu
The Lat-Lng coordinates will be automatically populated in the search input box and usually, the address will also be displayed in the dynamic side-panel (and very often a Street-View photo).
If you are looking for a way to query for the coordinates, you can use the Geocoderdev-guide service to turn addresses into coordinates.

Have you looked at the geocoding API for google maps? It allows you to pass in an address, and returns a Latitude/Longitude pair in response, there is an accuracy value returned with each response to let you know how close the geocoder was able to resolve the location. https://developers.google.com/maps/documentation/geocoding/

Get Geopoints of <insert storechain> stores?

Is there a way to get all the geopoints of a storechain's stores?
If you f.e search for Ikea, walmart etc I would like to gather all the geopoints from the locations that google map or any other tool plot.

you might want to look into the google api license for geocoding . basically you would be doing a name search to get an address and then geocoding to get the gps, but the google api has some limitations on how you can use the service like how many requests per day (2500) and you must show that data on a google map, etc