Scan and Print

1. Dot per inch = D P I, Scan is more important than Print ... the higher the SCAN DPI, the more detail of the scan it is ... similar to Print, but print is restricted to the paper size, so 600 DPI should be more than enough.
2. Photoshop/Paint shop Pro/ TWAIN driver will take care of that for you, your printer also know how to take care of resolution ... you don't need to worry much about it...
3. correct, the higher the DPI, the more detail, but the slower the scan, and the BIGGER the file, since more information to collect and store.
4. You need a photo scanner, a professional one, HP/Canon have some high end scanner ... that do it great, but if you have the home-use one ... all you need to do is get the max DPI to get the most out of the original ...
But all depends on the original, if the original is not that good resolution, scanning won't do magic ... to enhance it ...