I don't agree with Brad. I would say "I have also been there", but "I also have a car". The reason is that the first sentence is in Present Perfect.The position for the word also goes between the Have and 3rd form of the word. However the second sentence is Present tense of the verb "to have" and so the also goes before the verb.

"Also" should come before "have" in both cases. It is an adverb, and they generally come before the main verbs. In addition, your first example is in the present perfect tense, and so the "have been" shouldn't be split unless you're using "never" (i.e., "I have never visited Portugal").

That's a little tricky, possibly. I can only say what sounds natural to me. To me - 'I have also been there' sounds more natural than 'I also have been there', although both are OK. 'I also have a car' is OK, 'I have also a car' is not, but 'I have also got a car' is the most natural form!