Those are scapes, and there are a couple of different approaches to dealing with them. Some people leave them to curl up as the garlic matures, and then un-curl when it’s ready to lift. Others cut off the scapes when they’re young and cook with them. Some do some of each.
Your garlic will die back from the top when it’s ready, and the untended scapes will straighten out. Lift a couple then and see if the cloves aren’t distinct, but still tight. They won’t separate easily until the garlic has cured for a few days, unless you let it stand too long before lifting it.
I don’t feed garlic heavily, but I do work some milorganite into the soild when I plant, and then I mulch with compost, so it gets some food. It likes plenty of water but needs to be well drained.