I really need some advice for a friend who has found herself in some bother

My friend got married to a guy she knew back from her parent's home town in West Africa, She is a British citizen herself (Born and raised).
They met on her many visits to the country and after talking over skype and the phone for about a year, they decided to get married in West Africa. I was very weary of the whole thing as I have known many people to get stung by Africans wanting to be with people who have a red passport (not all just some).
Anyway after they got married the husband wanted to come here (my friend didn't want to live over there) so he put through his application for Spouse visa. At first they declined it due to one person at the office not doing their job correctly but it set back his arrival by about one year. Within that time although they were in contact my friend's eye started to wondering as she was lonely (no excuse i know) When he finally did arrive early last year i guess their feelings may have slightly fizzled out but they intended to make it work.
Now my friend lost her job and decided to go Uni the same year he arrived so now the support she was suppose to give was proving difficult and he was allowed to work on his visa but was finding getting work difficult. My friend then met some guy at our friend's wedding and had a one night stand while her husband was away at his sister's.
She kept this from him until she discovered that she was pregnant with the other man's child (oh the scandal). As her and her husband have not really been getting it on she knew it was the other man's child (she told the other guy and he wasn't interested throughout the pregnancy). She told her husband who was happy until she mentioned it wasn't his.
Mad as it sounds her husband vow to stick by her (I personally think because of his papers) then eventually the other guy said he wants to be there for the baby so her husband decided to leave her (but they are still married just separated)
He left her before the baby arrived and he hasn't paid one bill in her house even though he is working (on and off with agencies and his own business he is trying to set up which makes hardly any money) since last year. She applied for tax credit as she was part time work(16 hrs) as well as uni, but she applied as a single person.
As far as she is concerned her marriage is over (she is not with the other guy, he is a on and off dad) she is a single mother with a child outside of her marriage with no financial help from anyone. Her husband's letters still come to the address which he collects every now and then but they are still not 'together'. He is currently staying at a friends house.
I think he is keeping them married for the fact that by very early next year he has to put in his ILR and is stringing her along because she wants to make it work.
Here is what we need advice on:
She applied for WTC and CTC as a single person and didn't state she was separated due to the complication nature of her relationship, but as i said his letters come to her address so now the HMRC wrote to her and are asking what is her relationship to said gentleman.
As he is subject to immigration and can not apply for any benefits but she can, it isn't his child and he doesn't actually stay there or pay any bills, was she right to apply as she is single?
What does she say to the HMRC?
I really think this relationship is over and he is now using her.
What does she have to do? She is told that as long as he is married to her he has every right to stay here. They got married 2 and half years ago and as i said he came here early last year
(Sorry it's so long, Just needed to give you the full extent of this mad story)
And no the father does not help out financially either