12V limits the available power -
Power can be calculated as Voltage squared/Resistance.
That's RMS voltage... With 12V power suppl and a "regular" amplifier that's 12V peak-to-peak or about 4V RMS, or with a bridge amplifier you can double that.
So that works-out to about 4.5V with a standard amplifier or 18W from a bridge amplifier (with a 4-Ohm speaker).
(High power car amplifiers have a built-in voltage booster.)
It depends... The "regular Arduino" doesn't have a DAC, so no true-analog output. That's OK for square waves (like the tone() function as long as you put a capacitor in series to block the "DC component" (to make a square wave that swings positive & negative like a regular audio signal. Many amplifiers already have a capacitor on the input but if you're not sure, add one.
If you're using TMRpcm that can potentially be a BIG PROBLEM. It's actually putting-out PWM which is "nasty" high-level high-frequency signal that can potentially do "bad things" to an audio amplifier. I wouldn't use TMRpcm with my good stereo amplifier.