Между прочим (lit. among the rest) doesn't sound right here. It's more of a narrative sentence when used as a prepositional . However, кстати is universal and used very widely.
Thanks. When I learned между прочим (back in the stone age) I learned it as meaning "by the way" (same as кстати), but at the time I was reading a lot of Russian that was more than 100 years old, so I suspect I have a lot of archaic usage in my head.
It's a form of "сколько времени". It's considered wrong. However, I'd say the wrong form is more popular that the correct one. "Который час" is the most correct and least used form of asking the time (it sounds oldie, I guess).
No, it shouldn't be accepted, because it's incorrect. "Сколько время" is ungrammatical. It should be "сколько времени".
Just because some native speakers speak like that doesn't mean it's the norm and fits for educational program.