First, is it acceptable for a run to reload levels to get acceptable optional objectives as long as the timer is still running (i.e. not have that horrible dirty sink objective)

Second, when doing VR, are we allowed to carry 4 items to various places?

Edit: In team matches if one person dies, can you still submit the completed run if the recorder didn't die?

Yes to all three.

If it isn't mentioned in the rules, then generally you are allowed to do it.