1. No, the use of 'of' is not redundant in that sentance (also, it is spelt persuassive).
2. "All I have to do is to learn English" is correct; whereas "All I have to do is learning English" is not, because learning denotes a process that is occuring at the present time, whereas the context of the sentance places the action of learning English, in a future time. Essentially, the tense of the context needs to match the tense of the words.