I am brandy-new at bonsai, but not growing stuff, but I still have questions since this is a little different than growing a vegetable or flower garden; and I didn't find much information from searching so I am just going to see what I get for answers.

I just planted my seeds about a week ago and have some good sized sprouts from my poinciana already. They're currently growing in my makeshift greenhouse with a grow light. All of my plants in there are thriving and patiently waiting a better spot, but in the meantime I want to make sure I am going about it properly.

Is there a specific height I should look for or number of leaves before I replant them into a larger forever(ish) home? Should I only use one per pot or can I train them together to intertwine? I don't want them to choke each other out at the root. Last, how old should they be before I start to give them fertilizer?

You can see in the pic that I have a few sprouted and from the looks of the soil bulging I may have a couple more to come before I pick the one(s) that look best for growth.

There are many possible answers, all good. There are plenty of trees 4 inches/10 cm tall and there are plenty five times that. Most bonsais are single trees, but there are very good specimens with three trees, five, and forests with over a dozen. I have a picture of my wife and daughter in law standing under a bougainvillea cascade that comes down almost five feet/1.5 meter. There are almost too many artistic choices.
You can't do much right now other than keep them alive. Look at lots of pictures here and on other sites, and when they are a couple of years old you should start looking at individual trees, seeing the hidden bonsai struggling to get out.