I have some data in PostgreSQL which I am exporting to Amazon RDS service. Will I be able to use PostGIS extension in AWS, Also will I need the mandatory column "geom" or I could run queries with just latitude longitude valuies?
Yes, you will be able to use PostGIS with RDS. See Amazon's user guide on Working with PostGIS.
It appears to be the full, unmodified extension, so I would assume it operates just like a non-cloud installation. You'll still need a geometry column in order to run spatial queries.