In instruction manual for 2GIG-FF-345 i saw the say to use equipment code 0637. But this code has name HW D/W 5816. Is this a corect code?
Yes, it is a holdover from the original Encore Firefighter manual, but equipment code does not in most cases have any operational impact. Best to follow manufacturer instructions.
Also what code should I use with honeywell keyfob 5834-4?
You would just use 0577 - Existing Keyfob.