I learned that て form is used to combine with lots of things, but when putting て form with one other thing, it normally means ... and .... So why does putting て form with ごめん or すみません make it sorry for .... For example, if I put おいしくてごめん into google translate, it says sorry for being delicious. Is google translate just wrong? If not, then why is it FOR used in the sentence. If put おいしくてこんにちは, (which makes no sense, but こんにちは is also another expression) google translate puts that to delicious and hello. ありがとうございます
Both are possible. "-てごめん" is a valid template to translate "sorry for". Example: うるさくてごめん (sorry for being noisy / for the noise [I'm responsible for]). It's possible to use て form to mean "and" in a similar construction, too. うるさくて、ごめん、よく聞こえなかった can mean "it's noisy here, and I'm sorry, I couldn't hear [what you were saying] well". In both cases, what is noisy is made implicit, and must be supplied by the context indirectly. (In other words, you need to take the context into account to distinguish.)
おいしくてごめん is kind of a playful phrasing that "apologizes" that something is too delicious. That something can be a guilty pleasure food, for example.
Because the te-form does whatever the verb linked to says it does. There are many verbs that link to the te-form that have some special semantics in how they link to it. This isn't much different from how the ing-form in English usually links in a generic way, but various verbs have a special way to link with it.
For instance “ナイフを使ってパンを切る。” simply means “I cut bread using a knife.”, nothing special going on, but “ナイフを使ってほしい。” means “I want you to use a knife.”. Likewise, in English “I start running the car.” has special meaning. In both languages, a comma can be inserted to remove the special meaning. “I start, running the car.” restores the original one, as does “ナイフを使って、ほしい。” which simply means “I want, using a knife.” again. In both cases it's hard to think of a concept where the decoupled meaning would be used, but it exists in theory.
This is simply how both “ごめんなさい” and “ありがとう” work with the te-form.