Question: Let's say my girlfriend has made me/us dinner and I want to compliment her for her cooking (while we're eating). Would all these be equally correct and idiomatic?

It tastes wonderful, honey.

It tastes wonderfully, honey.

It's tasting wonderful, honey.

It's tasting wonderfully, honey.

Answer: 
> 
> It tastes wonderful.
> 
> 
> 

The verb "taste" is one of the verbs that can act as a linking verb, to connect a subject and an adjective. In this linking form, you should normally use the simple present tense (unless you particularly want to emphasise that that it will soon not taste wonderful) and use an adjective, not an adverb. The word "wonderful" describes "it". It doesn't describe the action of "taste", and so you would not use an adverb.
Take a look at the following examples:

I'm tasting the food. It tastes good / wonderful.

I'm smelling the flower. It smells good / wonderful.

It feels wonderful.

It looks wonderful.