Homemade stationary bike

That's actually a bicycle trainer. My ex used one hours at a time for about a year before her bicycle trip from CA to PA.

I'm cornfused.

I see how the rear wheel sits on the 2 rear rollers and can roll on down the road, so to speak, but what about the front wheel?

Does it sit in the gap between the frame and the front roller or is it just sitting on top of the front roller? There seems to be a gap between the frame and the front roller but it's hard to tell from the picture.

If it's just sitting on the front roller, is it safe? It seems that it wouldn't take much of turn (like in a moment of distraction) for the front wheel to slip off of the roller.

The front roller is normally a little bit in front of the front wheel, this one looks like it's centered on top of it. The purpose of the front wheel roller and belt is to make the front tire spin and giving it the all important gyro and steering action. It would be hard as hell, probably impossible to stay upright if the front wheel wasn't spinning and able to steer side to side.

If you mean the front wheel could "slip" off the left or right sides you are correct. This isn't an easy hop on and peddle exercise machine, it's a trainer. It takes some skill to master it, I know, I tried one and quit before hurting myself. My daughter could do it but I didn't want to break any bones. It's much more difficult than just riding a bike.

Quite correct that this trainer is not for aerobic training, but for smoothness of style after fatigue starts setting in. Of of the things you need to practice before getting on one of those rollers is getting a very smooth and stable pedaling style Although, if you can ride a back "no hands", both coasting and pedaling, mastering one of these becomes a lot easier. There is a version of this upon which you can install a fan to provide incremental resistance as you crank up the "stroke".