How to correctly say you liked some food?

Your examples were correct; hers was not, because in her example you are the object of the verb taste. That means you're the one being eaten, and the cake is the one eating you.

Both of your sentences were perfectly good ways of asking if someone enjoyed the cake. A good response might be, "Yes, it was delicious!"

"Taste" is one of a number of verbs of perception which have two meanings, an active and a middle.

In the active sense, it requires a direct object, and is said of the experiencer:

I tasted the cake.

It refers to the act of perceiving, not to the quality perceived.

In the "middle" sense, it must not take a direct object, but an adjectival or adverbial complement. It refers to the foodstuff, and describes the quality of what can be perceived in it:

This cake tastes sweet.

So "*The cake tastes me" does not make sense.

"Feel" has exactly the same range of meanings.

Saying "Did the cake taste you?" implies that instead of you eating the cake, the cake ate a bit of you. This is incorrect. Perhaps a better way to phrase it would be, "Did the cake taste good to you?"

Your other two options are correct. They sound natural to me (Am.E. native speaker).