Since you have never been married then no, you will not get any kind of spousal maintenance. In fact, even if you were, its very unlikely unless you were married to the likes of Macca that you'd get maintenance.
Your partner is still obliged to pay for the kids though. When you put the figures into the CSA calculator, did you account for the nights he may be having them? He gets a reduction for that.
The rest of the living expenses as you put it will come from tax credits, income support and/or housing benefits (depending upon your circumstances).
Since the house is in joint names then you are entitled to a share of the equity. The STARTING point unless you have an agreement or have held the house as Tenants in Common is 50-50. (The default is joint tenants). If you don't know which it is, chances are its joint tenants since for TiC you'd have signed another contract (Declaration of Trust) which you should have noticed will define a split.
HOWEVER, in practice it will depend on who's paid what and how long you've shared the house for. For example, if your ex put most of the equity in and you've only lived together for a short time then he'll get more than 50%. If you've contributed equally then its 50-50.
Unfortunately, since you are not married, courts will not take looking after the kids into account when deciding the split as this becomes a land law issue rather than matrimony.
FINALLY.....I don't know what your personal circumstances are but I'll say this. Are you 100% sure a split is inevitable. Sometimes people think splitting up will solve their problems but often all that happens is you are left dealing with a different set of problems. Make sure you explore all avenues such as counselling, lean on family/friends to mediate etc. before pulling the plug.
Good luck with whatever you decide to do.