Using MongoLab Database service vs Custom web service with MongoDB running on AWS
One thing to consider is that you don't need to use MongoLab's REST API. You can connect directly via a driver as well. 
So, if you need to implement business logic (which it sounds like you do), it makes sense to have a three tier architecture with an app server connecting to your MongoLab database via one of the drivers. In your case it sounds like this would be pymongo. 
-will
I am looking for feasible solutions for my Application to be backed with MongoDB. I am looking to host the MongoDB on the cloud with a python based server to interact with the DB and my app (either mobile/web). I am trying to understand how the architecture should look like.

Either i can host a mongoDB on the AWS cloud and have the server running there only. 
I also tried using MongoLab and seemed to be simple accessing it using HTTP requests. but i am not sure if it exposes all the essential features of MongoDB (what ever i can do using a pymongo driver)?  Also, should i go for accessing the MongoLab service directly from my  application or still i should build a server in-between? 

I would prefer to building an server in either case as i want to do some processing before sending the data back to application. but i am not sure in that case how my DB-server-app interaction design should be
Any suggestions?