Does the expression head over heels mean the same as head over feet? To be madly in love with someone?
The phrase is definitely head over heels - to be madly in love with someone typically used to describe a "new love" or "like a new love" condition.
head over feet is never used this way. In fact as far as I know head over feet has no special idiomatic meaning and I can't come up with a situation where those three words would come out of my mouth in that order except for when reading this SE question outloud.
(As an aside- this is where Urban Dictionary and the like must be taken with a grain of salt because it does list head over feet to mean the same as head over heels, but no native speaker I know would ever utter it.)