Evidence of a relationship is a way of establishing that there is a genuine desire for the person to visit the UK as a genuine visitor and not likely to disappear once here and start working cash in hand.
There is a section on the application about income. We usually check the 'supported by partner/spouse' option and explain in the further sections how I support my partner and, as in this covering letter, explain further that I will continue to do that while she is in the UK.
Whilst it is indeed not an English test, it is a formal letter to a government department and it does look better if words are spelled correctly.
To be honest, I think that the fact that you haven't known her for very long, have only met in person once, and have already had one visa refused, is going to make this quite a difficult application.
Its good that you are going to include as much evidence of your ongoing relationship as possible, but given the points I've made above, it may well be that you might get another refusal.
Good luck with it all.