1. It won't affect your application in the slightest
2. I don't think it really matters where you put it - I think other people have put their cover letters in the OTHER section? They may even look at the online form before they look at any of your documents anyway.
3. No, you don't need to cancel the application. Just include a note/cover letter stating you made a mistake and what the correction is and then move on.
If we were still using paper forms instead of submitting online, all you would have needed to do was cross out the incorrect date and write a correction in pen next to it on the form... so this is really nothing to worry about at all.
After submission, which number should I send to my university so they can check my right work for them? I noticed there are two numbers:
One from email of payment confirmation with a Ref number: UKVI_2SAA0*******
One from application form with UNIQUE APPLICATION NUMBER: 1212-0***-***8-****
I don't know for sure (since I think you're the first person I've seen to ask this question), but I would guess it's the Unique Application Number, since the other number just looks like a payment reference.
If you're not sure though, you could just give them both numbers and they can see which one works when they go through the Employer Checking Service form.