Tyres - width/tube/pressure

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I've got a MTB with Weinman Zac-19 rims and I'd like to fit them with GEAX
Street Runner 26 x 1.60 tyres.

1 The man at the bike shop said that 1.60 wide tyres would fit on my rims.
How do *I* know that?

2 I've read that the GEAX Street Runner should be inflated to 100PSI. Will
a standard car pump at the garage inflate to this pressure?

3 Will a standard bike tube (1.50-1.90) be okay, or should I get a special
tube?

thanks

1) Most mtb rims will accept 1" to 2.35"
2) The 1.6" has a rating of 45-75 psi, the 1.25" has a rating of 65-100 psi. I don't know if a garage car pump can produce that or not.
3) The tube should be slightly less than or equal to the tire size, so theoretically a 1.5" to 1.9" tube should work for a 1.6" tire.

Most garage compressors can produce about 120psi but may be regulated lower to suit their needs.
A bicycle floor pump is a good investment for any cyclist.