Yes it should be just fine for a compressor but steel or stainless screw together fitting would be a lot better more reliable
You want a small diameter rosin core (flux core) solder for electrical use. Must be a non corrosive flux. This solder needs a flux. Its also too big in diameter in my opinion.
This is a tin alloy (soft solder); yes, it can be made to stick to stainless, but it is not 'easy' silver solder, which is probably what you intend. Jewelry making supplies stores will have a range of 'easy' to 'hard' silver solders, if you only need a small quantity. For stainless or other nickel alloys and soft solder (i.e. moderate temperatures) an acid flux is required, the hard-solder 'salts' won't be active enough.
For a durable bond, 'easy' silver solder is very different from this (wich is tin-based soft solder). It is suitable for soft base metal joining, in some jewelry fabrications.
Solder is sold by weight, not length.
Most plumbing solder is mainly tin. Silver is usually less than 5%. Beware of any answers given by communityanswer because they are often totally wrong, such as saying this solder is almost 100% silver. Based on the spot price of silver, one pound of it would be about $250 today. The melting point of pure silver is 1761 degrees F, while "silver" solders melt at about 450 degrees F. Good luck soldering pipes with pure silver.
Yes, it can be used to join two pieces of brass together. Make sure your brass is clean.
Better off cutting and putting a sleeve over the spot you cut and soldering it