How would iconnect my Arduino Mega to house Mains, without buying a transformer, and having to make a whole setup for that. Can i just use a regular phone adapter? Or is 1 Amp too large (or 2 Amps).
Amps tell you how much current you can draw from the power supply, or "how much it can do".
You can hook up 3Amps power supply to a device that draws 1Amp and it will work ok, still having 2 amps of reserve.
You must pay attention to power supply voltage and keep it in specified range.
Arduino Mega has recommended input voltage of 7-12V, so you must deliver at least 7V. There are plenty of cheap wall power supplies with voltage regulation from 1.5V to 12V.
How much current it will draw depends on your application, but I doubt that you can suck more than 0,5-1A in a typical application.