The sentence is written perfectly. In this case, I would use "by your side" in the blank space. "By your side" is very intimate, and implies that you have a close connection with someone and that you will support them. "With you" can just mean "together," and can be used sometimes for intimate connections but also to mean that you'll just stay with someone while they walk through a supermarket. "With you" can be used for intimate or casual situations.

As for 1) and 2): Changing the tense changes what you are saying and when the events happened. I explain below: I might not have been here from the start: means maybe I wasn't here from the start but I will stay by your side till the end. Sounds something that happened in the past I may not be here from the start, but I will stay ....... : means maybe I won't be here from the start.. Sounds something that will happen in the future and maybe I will not be here when it starts in the future but I will be till the end