Electronic – DC motor causing noise on the power line

You should always put a capacitor across the motor terminals even if your circuit is not affected, because brush arcing creates rf noise that can interfere with other equipment (eg. AM radios). The usual recommendation is to install two 0.1uF ceramic capacitors, one connected from each motor terminal to the case. This 'grounds' the case to rf without the danger of having an exposed DC connection.

Ripple can be a problem for sensitive equipment which has poor power supply rejection, but normal filter capacitors and regulators will usually eliminate it. Another concern is the current spike and voltage dip that occurs when starting the motor. This motor has a stall current of only 390mA, so provided your 12V supply can handle that you shouldn't have to worry about it. Just make sure that the motor and its control circuit is wired directly to the power source, and run separate wires to the other devices.

The catch with low cost audio chips like this (or even the more expensive LM1875) is that guaranteed PSR is rather low, around 50dB, while the typical one can be much better (90dB promised in the case of LM1875, see below).

The TDA2030 is actually even less promising with only 40dB guaranteed and 50 typical:

And TDA2003 is even worse with 30/36 dB min/typical:

That's definitely going to be audible if the power source is noisy. (Also beware that these numbers aren't quite directly comparable because ST tests at 100Hz noise and TI at 1kHz...) So... if a linear regulator supply is out of the question (which will totally kill any audible noise from that source in my experience [it gives you some guaranteed 90dB with a LM317/LM337 solution]), try a different TDA2030 chip, assuming you're not having fakes or the CXY knockoffs (or try a LM1875 as it's pretty much a drop-in replacement). Luck of the draw with these things.

Your unspecified "cell phone charger" is almost certainly an SMPS with atrocious noise characteristics (better ones exist, but usually not at this price point). See for example what cheap ones have inside: https://www.youtube.com/watch?v=wi-b9k-0KfE

Also, a linear regulator after an SMPS won't be anywhere near as effective as one after a "classic" (filtered) rectifier. The reason is that the typical linear regulator is very good at eliminating mains hum (actually 2x the mains frequency in a bridge circuit), but its performance gets a lot worse starting around 10kHz... and that's exactly where the SMPS noise usually starts. And the audio amp IC has similar curve, e.g. here's the one from the LM1875:

Summary: the guaranteed fix is better (preferably linear regulated) power supply, which you can build yourself. If that's not an option somehow... try the amp chip lottery. However no amp chip will will magically eliminate the horrible noise put out by a super-low cost SMPS.