Should I use a hose clamp on the furnace drainage pipe

Don't bother trying remove the drain. Don't try to renew the putty, you'll just have the same problem again.

Remove all the old putty you can. Roughen the surfaces that contacted the putty with coarse sandpaper. Clean the shower base and drain surfaces where the putty was a well as you can. Fill the resulting gap with self-leveling polyurethane sealant. Do so in a way to not trap air and to fully fill the void. Once that stuff cures, it'll never leak again!

If you do have to remove the drain in the future, simply cut thru the sealant with a sharp knife.

You are going to need an adapter to get the hose attached to the compressor, then another adapter to get the compressor nipple attached to the hose. The adapters look like this:

This nipple comes in a variety of sizes, so you have to match it for intended usage. This nipple will go into the coupler on the compressor and female threaded end would be attached to the top end (as looking at the picture) of the hose. You'll need another similar nipple attached to the end of the tool end which looks like this:

You'll notice the big difference here is that it has a male threaded end. This (obviously) will go into the female threaded end on the tool.

These adapters can be made out of brass, aluminum, or what have you. For best results, I've used Teflon tape around the threads to minimize air leakage.