This is an example of a word with irregular usage. I believe that Italian has a lot less irregular words compared to English. Unfortunatley English is full of irregular words. English children when they are growing up, pass through a phase where all the past tense words are the present tense with -ed (as in do doed) and more tasty is heard. This is called an over regularisation error and persists until the child become familiar with all the exceptions. However, we adults still do the occassional lapses so don't feel bad about your question, we all understand.

No. The word is tastier. Some words allow one to use more and some add er to the end: smarter, stronger, nicer, bluer; lighter, heavier, etc. More is used when it isn't appropriate to add er to the end of the word, such as more transparent, more decorated, more finished, more excited.

Even so, I don't think I've heard many people (in real life) say "tastier". Much more natural : I prefer this one, I like this one, this one tastes better.

You would say tastier.