Would it be correct to say "Chwe" instead, I've heard some North Walians say it this way before.
That form is used before certain nouns, so it could be considered an alternative form, but if you asked them to translate "Six" into Welsh they would say "Chwech".
Is there a rule to know what nouns use "chwe" and which ones use "chwech," or is it something you just kind of have to figure out with exposure to the language?
This is copied from the "lesson" underneath the chapter buttons if you use a browser and not the app: "(Note - known error - pump, chwech and cant (100) drop their final letters (-p, -ch, -t) before nouns, Unfortunately this has not been done in all examples on the course yet and you may sometimes be presented with incorrect examples. Please do not report the errors when you come across them - they will be fixed as soon as possible. We cannot easily get rid of them at present, but they will vanish when we release Tree2, the next version of the course. The correct versions will always be accepted in your answers.)"
Would I be correct in thinking this word has to do with the German Sechs?
Numbers tend to be similar across all the Indo-European languages, so yes, although "Chwech"'s closest relative is "Hwegh" in Cornish.