Bogen, good questions.
A repeater extends the range of weak portable stations. Ham radio is in a sense divided into two ranges, The HF (high freq) bands (160-10 meters) can go very far. They can do this because these frequencies tend to bound off the earth’s atmosphere. Therefore like a giant mirror in the sky, your signal can bend around the earth to the other side. In addition, usually these transceivers are very powerful and bulky and use a lot of power and big roof-mounted antennas (but do not have to). They also have a very short wave radio-like sound with a lot of static and crackle, etc., and different people may be on same freq which causes one to drown out the other.
There are also the VHF (very high freq) bands which are 2 meters and 70 cm and above (remember that the smaller the wavelength the higher the freq.) These bands are mainly line of sight which limits to about 50 miles max with the best antenna, but if there are buildings or obstructions, then much less than that. In addition, they are usually used for portable walkie-talkie (HT=handy talkie) sized devices which are weaker, and have small antennas. The method of modulation for these is usually FM which is much clearer and without static. In addition, instead of a continuous freq dial, there are usually well-defined slots (like channels) which prevents people from getting on top of each other. Practically, about 2-3 miles I believe is the best you can do directly (simplex) with most of these portable units. In a car, where the roof blocks the signal from getting out, it can be less.
For this reason many clubs sponsor repeaters which are very powerful stations mounted on tall buildings that rebroadcast whatever they hear. This allows many people in cars to be able to speak to each other. They rotate if there are more than a few people at one time. The range is now about 30 miles. A mag mount is an externally mounted magnetic mount for your car to allow the signal to get out of the car better. (Listeners on the repeater sometimes get annoyed of someone is weak and breaking up and 25 other people can’t hear what he is saying.)
While some transcievers can cover both of these ranges, they are not that common, and generally you would be sacrificing the portability you want on the high bands. (Remember, before cell phones, hams were happily talking away with each other on the road when it was only a pipe dream for everybody else. There were also no laws then about not talking while driving. The good old days.)
Will answer the rest of your questions shortly. Need to take care of something now.