Using adhesive tape to capture the metal dust is the best way to clean magnets.
No, once a magnet is fully magnetized (saturated), it cannot be made any stronger.
No, neodymium magnets do not require a keeper for storage like Alnico magnets.
There are several simple methods that can be used to identify the (Scientific) North and South poles of neodymium magnets.
1) The easiest way is to use another magnet that is already marked. The North pole of the marked magnet will be attracted to the South pole of the unmarked magnet.
2) If you take an even number of magnets and pinch a string in the middle of the stack and dangle the magnets so they can freely rotate on the string, the North pole of the magnets will eventually settle pointing North. This actually contradicts the "opposites attract" rule of magnetism, but the naming convention of the poles is a carry over from the old days when the poles were called the "North-seeking" and "South-seeking" poles. These were shortened over time to the "North" and "South" poles that we know them as.
3) If you have a compass handy, the end of the needle that normally points North will be attracted to the South pole of the neodymium magnet.