1. 7.5 is definitely width.
2. Offset is basically how far away from the car's body the wheel is mounted. The higher the offset, the closer the wheel is to the center of the car. You have to be careful here, because you can't have the wheel too close or too far, since too much in either direction causes the tires to rub against the fender when you turn your steering wheel either way. Our stock wheels are 18x7 with a 52.5mm offset, I believe.
3. Wider tires will work, but it all depends on what offset you have and what size the wheel is. You basically should ask around to see what other people have gotten to work. Our OEM tires at 215/45/18, so you figure 225/45/18 shouldn't be too far of a stretch, but 265/40/18 would be very unlikely to fit. This is definitely where you have to play around with things and ask around.
4. There are a huge number of choices for you to make here. First of all, what kind of tires in general do you want? Summer? All season? Winter? This probably depends entirely on your location. If you're in the south, you can probably get away with using Summer tires all year round, but if you're in the north (like me), you will have to worry about changing out your Summer tires for either Winter or All Season when the snow hits. This probably means you want to consider using All Season tires 100% of the time to avoid this nuisance. Keep in mind that Summer tires are a TERRIBLE liability in the snow, since it will likely get you into a car wreck when you go sliding into the railing the first time you try to make a turn at >20mph in cold weather...^_^;
Once you decide what kind of tires you want, you can go to a site like
www.tirerack.com and figure out what kind of brands and models are good by looking at their ratings. This will give you an idea of what is good and then you can figure out what combination of factors are important to you (dry traction, wet traction, snow traction, road noise, and tread wear) and then just pick the one that makes the most sense price-wise.