I am doubting about wich of the following sentences is the right one, or if all are correct. Thaks in advance for your help and explanations.
a) 我可以试试吗? b) 我可以试一试吗?
c) 我可不可以试试? d) 我可不可以试一试?
All are correct, but all are not equally desirable. As a rule of thumb, any extra word that do not add meaning or nuance (emphasis, intonation, etc.) to a sentence is better left out. I would pick (a). The rest, in particular (d) seem a bit wordy to me.
Also, if you don't mind, I would like to mention another thing, which you've obviously learned already. But I would use this opportunity to point out for other beginning students who may be reading this answer.
(a) and (b) are what we call "ma" questions, and (c) and (d) are "yes-no" questions. "Ma" questions tag the question particle 吗 at the end of a sentence to turn it into a question. "Yes-no" questions use the form V-不-V and there is no need for a question particle at the end.