1) Is it right to say " I feel I can do it " or it is formally better to say " I feel that I can do it "?
2) What is the difference between " I do have enough money " or " I have enough money "?
Welcome to the forum, astra.
As your first question is about I feel I can do it, that would have been a better thread title.
Mr. is meaningless as a title.
1) Both versions are correct. The second is probably slightly more formal.
2) The sentence with do is more emphatic and may be used like this:
YOU: 'I'm going to buy a new watch.'
ME: 'You haven't enough money.'
YOU: 'I do have enough money!' (with emphasis on do).
In future, please ask unrelated questions in separate threads. You'll get quicker answers that way.
Rover