electrical noise problem with adaptor
I didn't see enough information to rule out any of those, and all should be fixed.  Of the three, only number two is likely to be fatal.  I'd go and buy a 3-wire receptacle tester, and verify your neutral and ground are correct.  You can probably pick one up for $10.  Having these fouled up is dangerous, and will cause noise, among other issues (like death).  If they are bad, get a qualified electrician to make the repairs.

Then, move on to number one, and get a decent shielded cable.  These don't have to be the expensive gold plated (literally) ones.  The lamp switch might be dirty, and causing a little spark.  These are usually well contained within the lamp itself, and aren't dangerous, but the spark can be picked up by the unshielded cable.

Doesn't your "adapter" have a transformer too?  I'd be surprised if it doesn't. I can't think how this might be involved with your noise related to a lamp switch, but you seem uncertain about it, so you might want to replace it.

Good luck!