VAC - VDC ... What is Polarity?... Imagine an hypothetical AA cell that keeps rotating its poles, the one that used to be the + then turns into -, and the - turns into +, X times per second, over and over again without stop.
On DC current, instead, the + stays as + and the - as -, always. Polarity doesn't change. Like real AA cells, or any other battery.
Got it?
Alternaing current, like the one that's coming out from your wall, changes its polarity 60 or 50 times per second, depending on the country.
Noise is caused by the relays continuously turning on and off, 60 or 50 times per second, because they are feed with AC. I guess it may fatigate the relays mechanical system, so don't do it.
You need a DC source, because Direct Current keeps its polarity constant, so your relays stay on or off as desired.
As I said, batteries are DC sources. For your application, you can also get a wall mart labeled as Output: x volts VDC, x mA
Your second Question
Using the 1000 mA source to feed (for example) a 500 mA bulb is not a problem, because the bulb will take the 500 mA it needs.
Leave a safe margin, i.e. don't use a 1000mA source to drive a 1000 mA load. That varies with each application. peak current etc... but on layman terms, more is better: a supply with excess of amps is better than one that lacks them