Is flux in solder?
In some solder it is. But even if it is in the solder you should still use flux.
Flux is used to keep metals from oxidizing. Solder will not bond well with copper-oxides which are formed when copper is exposed to high temperatures (ie a soldering iron) the flux prevents the oxidation. If you were to solder without flux the solder joint would be weak and possibly completely nonconductive.
When circuit boards are assembled, the parts are soldered on. In order for the solder to make a good connection to the parts and to the board, a substance called flux is mixed into the solder. It removes oxidation and cleans up the surfaces of the different parts so that the solder can stick to them. After the board is assembled, there is still flux on the board. Flux remover dissolves the flux and washes…
Solder has an expiration date because of the flux content. It does not go bad-per say, but the flux will dissipate out of the solder after a while. It's still useable, but the flux content may be slightly diminished. Also, over time the solder oxidizes. For home or hobby use, it's fine. But in a manufacturing atmosphere, you need to be prepared to throw some away every year.