#1 Will this modem transmit my xfinity cable tv or just internet????
This modem will not "transmit" anything, it is not a router and doesn't provide a wireless ("wifi") signal at all. It also does not provide a cable TV connection- you need a set top cable box for that - it just provides access to your cable systems Internet network.
#2 Mine keeps disconnecting after a month of use. Is it broken?
I would notify your cable company first it sounds to me that the wiring that goes into your house for your cable is old and needs to be replaced
#3 To get wireless WiFi can I connect this to a simple router?
This is simply the cable modem. Yyou can hook it up directly to a computer or to an internet router with wifi.