Is it OK to use a compression fitting on a hot water pipe? I have to install an air bleeder valve in the middle of a pipe and the area is tight and has electrical wires near the pipe, so I would rather not solder. I know that it is used for appliances, but I am not sure about the high pressure from heating system?

Should be fine if we are talking copper line. Many of your angle stop options for under the sink are compression on both ends. You 40-50 psi hot water will not blow one out that is properly snugged.

Not inside a wall. You could use a Shark Bite coupling.

Not inside a wall. You could use a Shark Bite coupling.

What would be the problem with using compression fittings inside a wall?

They have a slightly higher chance of leaking than Shark bite or solder. Not good if its inside a finished wall.