(1) Will he be able to make any changes to the app which is UP and running on the market place without logging into my developer account? I don't think so, but want to reconfirm.
(2) It looks like it is better to have the source code in case if i want to make any changes in the future. In this case, what kind of format i can ask him to send me the source code?
(3) I am not a programmer and don't know ABCD of game programming. So even if sends some thing, i cant really make sure that this the source code for this program. What are my options in this case except trusting him thinking that he is sending the right code?
1. As far as I know, only if the app accesses or uses external connections (e.g. if it connects to a server, and he has access to that server).
2. Source code is just a bunch of text files (which can different file extensions, it doesn't really matter). Basically, these text files are then translated into something which the device can understand. This process can often require some additional files, e.g. for setting some of iOS' target settings, etc. These additional files are sometimes called solution files, project files, etc.
If you want the source code, I would just ask him to send you the source code. He should know what it means. You might want to explicitly state that you want everything required to build a version, including all the necessary assets, etc.
Depending on what tools he used to create the app, you might need to download/install something in addition to what he sends you. E.g. Unity, or other game engines.
3. Find (or pay) someone to verify it for you. Alternatively, have him walk you through how to setup and build a version from scratch, using the assets and code he sent you.