Would multiple radio repeaters experience feedback or interference from eachother?
A repeater usually has seperate transmit and receive frequencies.  You would normally only have one repeater for a given transmit/receive frequency pair.

If you have more than one repeater operating on the same frequency pair, then you will get chaos.  Multiple transmitters on one frequency is just going to end up blocking all the receivers.



The way a radio system with a repeater works is like this:


You have two frequencies (I'll call them "low" and "high".)
You have a repeater that receives on "low" and transmits on "high."  Anything it receives is immediately transmitted.
You have a bunch of regular radios.  They transmit on "low" and receive on "high."  Note that this is the opposite of the repeater. When a regular radio transmits, it turns off its receiver.
The regular radios have a lockout - they aren't allowed to transmit while they are receiving.


Now, when the channel is free, one of the radios can start transmitting.  The repeater broadcasts it to all the other radios.  None of the other radios can transmit until the first has finished.

There is always only one transmitter operating on each frequency at any given time.

Your idea of an "analog mesh" would require seperate frequency pairs between each sensor, and the "route" through the mesh would be fixed by the pairs.

If you tried it using just one pair, you'd get transmitters stepping on each other - interference and lost signals is all you'll get.