Learn English – question about tense – “I barely finished the homework after he returns to the house.”

This is mainly a joke. There isn't a real tense in English to say "something that would’ve happened in the future of a past that was affected by something from the future," probably because no one has ever encountered such a situation. There's no grammatically correct way to combine tenses in this way.

If I had to make an actual "correct" sentence for this, I would say something like, "But it wasn't until his 21st birthday that 1955 Biff would have placed his first bet in that timeline." But again, there aren't really any rules in grammar about how to talk about time travel. If there were, maybe we had will could have used them.

The difference between bare infinitive and gerund (-ing) is one of aspect, not tense. The bare infinitive looks at an action as a signal point in time whereas the gerund looks at it as a process (which is currently happening).

I watched him climbing over the fence

This means at the moment you watched him, the act of climbing was still in progress. Compared to:

I watched him climb over the fence

This view the action as a signal point without a beginning or end. This distinction is typically called the imperfective vs perfective aspect.

The bare infinitive doesn't imply a completed action, but rather a complete action without further structure or detail.

Thus,

An uneasy feeling came over me as I watched him walk towards the revolving doors

means the uneasy feeling occurred as the speaker watched the act of walking in its entirety.

For many circumstances, the differences between the bare infinitive and the gerund will be slight.