Are there any decent, affordable devices to transmit a cable signal over a wireless connection ?

If so, what are the limitations ?

No can do, except one channel at a time after a tuning device.

Wireless senders have been around for awhile, most work in the 2.4ghz range and are prone to interference from numerous sources including your microwave oven, also as previously stated you are limited to one channel at a time.

I had used one in the past with good success, once you get the send and receive antennas oriented properly, and if you have a remote that is also rf.