Yes because the stem system which delivers water are still working.
Celery does have roots.
by roots
They store food in the roots
Is there a picture out there of how celery grows?
the type that's underground.
celery
Probably not. I am not sure, but surely, I don't see roots plucking out when I pull a cellery stalk.
Depends what kind of plant it is
Orchids do, they grow in a type of a fur barks but some roots do grow out and on top of the barks but mostly the roots are under, in the bark. There are some air ferns that grow out in the air without soil or anything. They need only misting with water daily.
no
Yes
Celery can grow in both hot and cold water, It helps only slightly for plants to grow in warmer water.