Irina's comment was roughly right, even if her grammar wasn't very clear. Without the 'to', the meaning to a native speaker is quite different. "Put me through someone" sounds like "Make me into a spear, and pierce someone with me".

Yes, actually we do need to use to in these sentences. In the fist sentence we use to at the and of the question because if preposition has a connection to the answer, it is a part of the answer, we need to put it at the end of the question. In the second sentence we use as we usually do when we use a verb with the meaning of direction like go, drive and etc. We can study it during the lesson, I can prepare pdf materials for this grammar.