Is my prayer valid if I pray in pants that have a hole, and it is possible that a part of the awrah might be exposed, while fearing that the prayer time might elapse?

If you enter into prayer having covered what must be covered, then your prayer is, in principle, valid. It is not invalidated merely by doubt concerning the uncovering of your 'awrah during it. What might be visible through a hole may be a minor part of the 'awrah, the uncovering of which does not invalidate the prayer according to many scholars.