Environmental destruction and overpopulation are basically the same thing.

We won't limit the growth of the human population. Eventually, all populations run into a wall in which the lack of resources limit population growth. This is going to limit our population. The question is whether we can overcome a billion years of evolution that pushes us to reproduce before our environmental degradation causes a massive crash. My answer is "no."

I can't answer the question about how society must change to support denser populations. I think if we're going to survive as a species, we're going to have to get used to the idea of lowering populations. I'm not smart enough to figure out how that's going to work. I'm not optimistic.

Humans will never send a significant number of persons off-world. I can't for the life of me imagine why we should. The solar system, and the universe, are cold, empty, lonely places. My guess is that we've gone as far as we're going to, absent some revolutionary technology advancement in the next few years.

I don't know about engineering our own DNA or new mutations, but I have been trying to train my skin cells to photosynthesize. Not much luck yet, but watch for further bulletins as events warrant.