Virtually means "almost (in respect to degree or strength)" or "almost completely".
In your first pair, the difference is very small:
This mission is almost impossible to achieve.
This mission is virtually impossible to achieve.
Here, I think virtually is a stronger choice, so the second sentence simply means the mission is more difficult than the first. Both sentences mean basically the same thing.
Your second pair has a much bigger difference:
He was almost killed in that accident.
He was virtually killed in that accident.
Here, the first sentence can mean either:
He was almost hurt in an accident, but he wasn't hurt at all. (For example, his car almost fell off a cliff, but it didn't fall. He got out safely.)
He was hurt very badly in an accident. He almost died from his injuries.
On the other hand, the second sentence (with virtually) can mean only the second sense. He was hurt badly and was close to dying.
Perhaps a good rule is to imagine that the adjective modified by virtually really is true, but then take a tiny step back:
He was killed in that accident. He's dead.
He was virtually killed in that accident. He's been in the hospital for a month.
For your system, the terms you want to use are:
Make: Toyota
Model: Corolla
Year (or "Model Year"): 2015
Plate number: AAA 123
Color: Red
Explaining why you need to use "make" instead of "brand" is harder than I expected, though. The words "make" and "brand" have the same meaning, we just tend to use one more often than the other when talking about certain types of items. There isn't always a good reason for why people use certain words.
When talking about your favorite brand of clothing, peanut butter, software, shampoo, or pretty much anything other than a car, you generally use "brand". For cars, you almost always use "make".
You would never say, "This is my favorite make of clothing".
"This is my favorite clothing-maker" also sounds a little odd.
For cars, people do sometimes say, "Here is a list of top car brands," but that could just as easily be "Here is a list of top automakers".
If asking or describing the manufacturer of a specific car, though, you definitely want make. As the text you posted points out, it just sounds odd to ask someone, "What brand is your car?" even though they would still understand you and answer the question.
Best Answer
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.