"In for a penny, in for a pound" means that if you're going to do something at all then you may as well do it wholeheartedly.
Vctory Ong“I am a person, in for a penny, in for a pound. When I have decided to do a thing well, I will do my best until the last minutes.”
The first sentence doesn't read very well, and "until the last minutes" is not idiomatic here. You could say:
I am an "in for a penny, in for a pound" kind of person. When I have decided to do a thing well, I will do my best until the last / until the end.
Vctory Ong “In for a penny, in for a pound. If I have decided to do a thing well, I will do my best until the last minutes .”
This is OK except, again, for "until the last minutes".
Edit: Sorry, I didn't pay enough attention. In both sentences you don't really need to say "do a thing well". It's mildly contradictory, because if you do something "well" then it's kind of obvious that you see it through to the conclusion, so the "if"/"when" clauses seem redundant.