Under normal circumstances, you will be issued a BP for both segments of your trip in Bombay. Your luggage will be checked through. You will not see your luggage in FRA.

You can use this:

http://www1.frankfurt-airport.com/cm..._frankfurt.htm

to find where you arrive, and where you depart. There is a shuttle bus, and a tram, which you can use, if necessary.

You will unquestionably have to go through at least one set of security. It is required by The FEDS(US government). They have their own very strict interpertaiton of the regulations they are enforcing(US rules, enforced by German Nationals)