700c wheels will probably fit. You may or may not need new brakes. Look at where the brake pads mount to the caliper. They should be held in place by a nut that is secured to a slider. If there is some room left to go down on the sliders, 700c wheels will probably fit fine. 700c wheels are slightly smaller than 27 inch. I would just keep the wheels if they are aluminum. Just take them to a bike shop and ask to have them trued and have the bearings repacked if you don't feel like messing with it. It shouldn't cost a ton for that.

I would just hit the corrosion up with a green scrubby pad then maybe wax over it with some car wax.

Just looking at your pics, that seat looks wrong for the type of bike. See how you like it but it looks too wide for a road bike. It's not a macho thing to have slimer seats, it's mostly to give clearance to your thighs. If it sucks, come here and ask for recommendations. Most people will probably say to get a brooks b-17 which is pretty much most comfortable all around seat ever made.