The game only check the fire in the beginning of the craft, but check light during the entire crafting period.
There is a “mark firewood source” in the construction menu (default key is ‘*’ I think? Not sure if I changed it or not). I think if you put your wood there and stand next to it (and next to the fire) during crafting, you’ll maintain the fire automatically, but I have never used it.
Do note that you can restart an interrupted craft by pressing the “re-craft” butten (default, ‘-’). So you can always just re-start the fire then re-start crafting.
For 5., the game doesn’t simulate dough or other itnermediate craft. It make sense that you don’t get anything until the batch is finished, after all that’s why a batch is faster, you make more dough and then cook it all at once.