Santa - she can see her priest and explain that her dh left her. They will offer marriage guidance, if her h won't go that's more evidence on her side. They do try their best to support a marriage and stop it from falling apart, but they also know that if one party refuses then there is nothing more they can do. I'm sure they will let her move on. Also, if she's living by herself and is not seeing anyone else, then she can still receive communion as she is not commiting adultery. However if he is seeing someone else then he is, and that is grounds for annulment.
zebra - if you sin, it's not just against the church, you sin against yourself. There are some things that the church deem to be sinful that are no longer considered so. For instance you wouldn't confess that you are living with a man and having sex before marriage - yet in the eyes of the catholic church that is still a sin.
Officially you are meant to cleanse yourself of sin before you receive communion, so that you are in the purest state. However the priest is not going to interrogate you at the altar is he?
If your conscience is bothering you and you'd like to get past sins off your chest, then I do recommend you go to communion. You do feel a lot better for it, you feel 'cleansed', like a weight has been lifted and you are in a better state of mind to receive him at communion. The priest is not there to condemn or to judge, he is there to listen and to absolve you in the name of Jesus. And of course whatever you say in the confessional cannot go any further, they take an oath on that.
There are certain circumstances in which you are not supposed to receive communion such as if you are divorced or if you are not a baptised catholic.
So to answer your question zebra - no you are not supposed to until you have been to confession and have been absolved. In the case of divorce however, if you are in another relationship then in the church's eyes you are repeatedly sinning, so confession would be of no use as you cannot be absolved of something you are not truly repentful for.