Learn English – Leave the door open vs Leave the door opened

Get through means "to suffer through."
To get through something usually means in an emotional state, like to get through a divorce, or to get through something challenging, like a test.

She was so tired that it was difficult to get through the day.

Go through means "to pass through something."
"Go through something" is the physical of "go through something," and it is always in the present tense, like "go through a divorce" or "go through a tunnel."

After you buy your token, put it in the slot and go through the turnstile. Go through the old city gates and you will see beautiful 15th century church.

So its always you go through a door, not get through a door.

I would not say that there is a difference in aspect per se, but the phrases would be used in different situations. The more common phrase would be "make someone wonder" which, as FumbleFingers phrased very well, would "set off a train of thought". I think most commonly one would say: "It makes me wonder [what he has been up to exactly]."

To "leave someone wondering" is a less common idiomatic expression which, to me anyway, implies that a person has intentionally left a situation or relationship ambiguous and that the ambiguity will, most likely, never be resolved: "I thought at first that we were hitting it off, but she left me wondering." (To use the other phrase: "It makes me wonder how things really stand between us.") I suppose it could refer to unintentional ambiguity as well, but in that case, I would more likely say "left me confused" or "left me completely lost". I hope this answer didn't leave you confused.