For the cable, you don't need to do anything special, its all connected together. Just connect the coax on the outside of the trailer and switch your TV to search for cable channels instead of over the air, and don't turn on the antenna power booster.
For the speakers just pull one out and look at the back of the magnet, it should be printed with the Ohm rating. However, matching Ohms isn't real important for a travel trailer. Lower Ohms simply draw more power. Its only an issue if you are trying to play music for the entire campground and the low impedance speakers draw too much power and burn out the head unit. I'd be less concerned about Ohm rating and more concerned about finding speakers that fit and still have a nice sound.
In most instances the receivers that came with a lot of trailers were just garbage. You can replace it with any decent automotive head unit. Buy a generic mounting kit with it and you should have no trouble mounting it. Anything in the $80 to $100 range will work nicely and most have axillary inputs now for MP3 players.
2013 Jayco Jayfeather X20 E, 2008 GMC Sierra 1500 Crew Cab Z71 SLE