Number 2 should be "stopped for a while". It is difficult to quantify these expressions, but "for some time" is usually longer than "for a while".
Student or Learner
For example, if someone asks me "Are you still doing ..."
1) I have stopped for some time.
2) I have stopped a while.
Are 1 and 2 both correct?
Do 1 and 2 mean the same thing?
If you have stopped for a while, the implication is that it is a temporary pause before you continue.