In general, if you are referring to a single, simple subject, like "the highway" and "being finished", it's usually easiest and most correct to use the simple future, which is just "will X" or "is going to X". For your first example question, either of the first two options is good.
The highway will be finished next year.
The highway is going to be finished next year.
They mean essentially the same thing: It will be finished. When? Next year. The third option,
The highway will have been finished next year
uses the future perfect (will have Xed), but it doesn't quite make sense. We use the future perfect to relate one thing happening in the future to another specific event in the future, but there is only one thing happening: the highway being finished. Saying will have been finished means that the highway will have already been completed, so it only makes sense in relation to something else. You would use the future perfect to say something like
The highway will have been finished by the time the President visits next year
For your second example, the most idiomatic answers, to an American English speaker, would be
I think it'll be finished soon
I think it'll be ready soon
The fourth one,
I think it is going to be finished soon
is grammatically correct, but it sounds a little stilted to this native US English speaker.
The third one,
I think it will have been finished soon
sounds strange, because, as with the sentence about the highway, it sounds like you're relating the finishing to a future event...but there is no future event!
Future Simple and Future Perfect
Future Perfect Simple