I'm not too sure about your mount questions, but I do collect working vintage gear. Here's what I do and look for...

If applicable, bring a battery - There's really no excuse not to bring a fresh battery for the camera you're interested in.

Bring a pen light - your cellphone light may also work. You just want to be able to really see inside the nooks and crannies. However, a pen light is necessary to check for light leaks (get the smallest light you can find, it needs to fit in the film compartment).

Study the Manual - Google the camera's manual and study up on the important features and functions, if you're not already familiar. Go into this with a testing strategy.

Look for Age/Damage - You want to get a feel for the age and state of the camera. Look for dust in the viewfinder and dust inside. Does the hotshoe look worn? How much brassing is there? Dings and Dents? There's usually some padding that the mirror slaps into when taking a shot - what's the status of this piece? Are there noticeable areas of grease accumulation?

Big thank you to Calyth for: Check for holes on cloth shutters - don't touch them, but hold them to the light to see if there are holes there.

Really study that manual before checking it out. This is particularly the case for old soviet cameras. They do not like having the shutter speed changed before cranking the film crank. You can / will break it if the speed is set prior to cocking the shutter.

Always err on the side of caution. If you're unsure about the camera, ask the owner for things you should not do or things you should be aware of.

Test Functions and Features - Remove the lens and open the back. Watch the mechanism move as you wind up a frame. Test every shutter speed. Double check the light meter by referencing another camera or light-meter reading. Test any other features.

Lens Tests - Add the lens back and double check that the aperture closes effectively at each f-stop. (use a longer shutter speed and look into the lens). Turn the focus ring from minimum to infinity and feel for grit. Look inside the lens for fungus and haze.

Camera being sold without Lens - Bring a lens for the body, if you can. Make sure that it connects without issue and also to make sure that there are no issues with the camera activating the aperture.

Light Leak Test - take the camera into a bathroom and close the pen light into the film compartment. Do make sure it's not applying pressure to anything and don't rattle it around. Wait for a few minutes for your eyes to adjust. Can you see the pen light? If so, there's a light leak.

Competitive pricing - Research the camera and what the average value is for a variety of qualities. After doing all of the above testing, you should have an idea what quality the camera is and what a competitive price for it should be. Negotiate/haggle as you see fit.

If you cannot do any of the above tests because you won't have the camera in hand before purchase or the seller refuses to let you test, then it's your judgement call.