I couldn't think of a reason why we don't conjugate the verb as in 'tenho' instead of using the infinitive 'ter', but it is rather common in Portuguese. - Espero terminar logo. I hope I finish it soon. - Queríamos poder começar depois. We wish we could start it later. Did you notice that in both sentences the two subjectives are the same? Perhaps that's why we don't conjugate it, it's already implied it's the same subject. If the two subjects are different, then the sintatic structure works just as in English. - Espero que terminem logo. ('que' is mandatory) I hope that they finish it soon. - Queríamos que pudesse começar depois. We wish it could start later. You could use that structure even when you have the same subject if you so desire, though some sentences do not sound as natural. - Espero que (eu) termine logo. (this one sounds perfectly fine) - Queríamos que pudéssemos começar depois. (this one sounds too long!) So your sentence would go like this: 'Sinto muito que eu tenha batido' and it sounds ok. Just remember you must use 'que' to connect subordinate clauses in Portuguese and the next verb usually goes in the subjunctive mood.

First, a little correction: "Sinto muito POR eu ter batido a porta do carro." Ok, now about the verbs: -- "ter batido" - it's a punctual action, completely in the past, before another action (in this case, the "action" is saying "I'm sorry", and the action in the past is "have slammed the car door") -- "tenho batido" - it's a continuous or repetitive action, also in the past, and it's not discarded the possibility of another occurrence in the future. If you say "Sinto muito pois tenho batido a porta do carro", it means "I'm sorry because, frequentely in the recent past, I have slammed the car door". Quite dramatic B-). Definitively it's not a stupit question! (And sorry if something is wrong/not-understandable in my english, fell free to comment/ask)

Sinto muito por eu ter batido a porta.

Because you conjugates the verb "BATER" in the past: "BATIDO". "sinto muito eu TENHO batido" gives the sense of continuation, but you have already slammed the door, past time, you are not hitting yet. I hope you have understood ... explain in English is more difficult.

The three example sentences you wrote in additional details are only correct if you use a similar structure to "Eu sinto muito por ter....". If you'd like to use use them by themselves you'll have to conjugate the verb "ter". Eu tenho falado com ele. Eu tenho estado muito ocupado. Ele tem estudado duramente. I must confess that those sentences doesn't really mean what you have assumed. This is the idea of what we really think when we read them: I have being speaking with him. I have being very busy. He has being studying very hard.