a. The farmer is ploughing the paddy field by using / with a cow.
b/c/d/e. The ox/cow/bull is ploughing (on) the paddy (field). -- All permutations are OK I guess, but it would be usual to omit the word "on", and I prefer to write "paddy field" in full.
Mr Wordy is absolutely right, but I just wanted to add an extra note about cow / ox / bull. In Britain (where I live), we usually only see cows (which is the name for the female animal) in the fields. Bulls (the name of the male animal) are much less common because they don't produce milk.
British people will often say "cow" without even thinking about whether they are talking about a m