a) Yes, you must not train a system without having correct, gap-free and recent historical prices. The files from the download page won't do. They are correct, but not recent.

b) You normally do not train a system for a particular broker. Only exceptions are systems that depend on certain broker parameters, f.i. a system that exploits rollover. Or a system that trades in different ways dependent on leverage.

c) Since training a system does not require a broker connection, you can train it on Sunday, on Christmas, or at any day you want.