Setting it halfway and measuring resistance from either outer lug to the middle should at least tell you linear or not. (Linear will be about half, log/audio will be much lower or greater, depending on which outer lug you're using.)
Sure. Set it to the ohm meter. Touch two tabs on the pot with the leads from the meter and slowly turn it back and forth. The reading should go up and down as you turn the shaft. Most have three tabs. If you don't get a reading on the first two tabs, move one lead to another tab. Most of the tabs have holes in them so you should be able to just stick the leads in the holes and leave them there for good contact.
The ohm symbol looks like an Omega symbol in case your meter doesn't have words on it.
Remember that there can be quite a tolerance on pot resistance values, (often +/- 20%) so don't be surprised if they are not exactly on a standard pot value.