Trying to create my own server and consuming it for code with my phone remotely (Mac OS)

Hi there! I need some help with this.

I have a 32gb Macbook Pro with the latest available update of Tahoe.

I'm using LMStudio with MLX to serve a local model and I want to expose it so that I can consume it with my phone to code and review stuff when I'm commuting to places.

These are my problems to solve so far that I need help with:

1. The mac turns off after some time. It doesn't matter what I set in settings. Have you found a workaround for this? using caffeinate or how?
2. I need an IDE / Agent editor that I can use to instruct the agent. I tipically use ZED from this pc, but I'm open to try something else that is mobile compatible.
3. How can I have the agent changes automatically deployed (usually it's websites) so that I can review and accept or reject the changes? when I'm working on my pc this is basically solved automatically because I'm working with local files.
4. Can LMStudio serve on the public internet or do I need another solution here? or maybe an extra step?

Thanks in advance!