What are the white tendrils at the bottom of these garlic cloves? Are they the beginning of new roots? I'm afraid they are indications of fungus or mold.
Those are garlic roots, no reason to worry.
If you plan to use these cloves, note that they are about to leave the dormant stage and start to sprout, so make sure you remove the green sprout in the middle of the clove. It is rather likely to have turned bitter now.
I found this video on youtube, which shows the roots forming on a garlic clove; in a rather early stage you can clearly see the little stubs your garlic has.
These are roots, just cut them off. Sometimes you might get a sprout coming out of the top, that's fine too.
Garlic sprouts after being exposed to cold, if you store garlic in your fridge it is likely to sprout, so store it at room temperature or a cool but not cold place.
I grow a field of garlic, your picture shows nascent roots. I eat the sprouts and have never noticed a bitter flavour.
If you want to keep your garlic from going off, wrap it in some kitchen roll at room temperature. The paper helps so much in prolonging the life of your clove.