Does all bluetooth modules support RFCOMM?
It depends on the module. There are absolutely no guarantees, because the modules contain their own embedded microcontroller and firmware which provides services.

You can get modules which have enough of the stack in their onboard processor that they do take care of RFCOMM and present as a serial port.  There are other modules (which are more flexible) and require the micro to talk something like BCSP and take care of the higher level functions such as L2CAP and RFCOMM.

You need to carefully look at the datasheet for the specific module you are looking at buying, and be especially careful because most of these chips are all identical except for the software running on them.