1. No. The gain/input level setting is adjustable to match a lower input voltage. It does not mean the amp will get warmer faster than if it had a higher voltage input.
2. There are different ways to get clipping. Signals get clipped when the output level of the device is turned up too high to match the input section of the next device down the line. A DMM does show you if the signal is clipped. If you're using it to measure the voltage coming out of an amplifier you can tell when it's no longer making more power as you increase the gain, but you can't tell precisely when it begins to clip. The only way to know is to view the waveform on an oscilloscope.
Another important thing about clipping: it can and often is in the music itself and there's no way to avoid that clipping without completely avoiding that music. You can have clipping in the music without it being dangerous, and the presence of clipping isn't always unpleasant to listen to.
You can get a whole lot of information on music, the way amplifiers and speakers behave, basic electronic theories and such by watching this video:
[video=youtube;85mWsMJOh-8]
