1) Yes, the diameter of a 700c rim (622mm) is 8mm less than a 27" rim (630mm), therefore the radius is 4mm less and that's how far you need to move the brake pads down. So the answer to your last question is to examine your brakes and see if the pads could be moved down by 4mm (about 1/6 of an inch). If they can then your bike is compatible with 700c rims.

2) The 120mm or 126mm is the width of the hub in your rear wheel. If you're just replacing the rim then this doesn't matter since you'd be reusing the same hub (which ever width it happens to be). If you're replacing the whole wheel then this dimension should match. Take the rear wheel out of the frame and then measure the inside distance between the rear dropouts - that is where the wheel fits into the frame. See if this dimension is 120mm or 126mm. Note that if your frame is steel then it isn't too hard to bend the rear part of the frame slightly to increase this dimension - but you want to do it evenly on both sides and it would best be done by a bike shop that has the proper alignment tools.

But I agree with other comments that you're probably best off just getting some decent 27" tires - at least for now. Back in the 70s we still had steel rims on our tandem and regularly pumped up the 27 x 1 1/4" tires to well over 100psi despite their 90 psi rating and had no problems with either blow-offs or pinch flats. I'd expect current Pasela tires to do just as well and you can get the steel bead version for under $15.