I really feel for you Zaza, this really is no way to live and like you've pointed out, it's a dreadful family dynamic and not great for the children.
There are far more informed Mums-netter's than myself on this subject but it sounds like you are in an abusive situation so perhaps give a call to Womensaid or a similar charity and they can give definitive answers to all of your questions. A good family lawyer would do similar but there may be a cost involved there.
I'll give none definitive answers to some of your questions based only on what I've read here, I'm not a lawyer.
If I was to rent anywhere with the children would he have to contribute financially?
Yes he would, it is not for him to decide if he can afford or not either. If he is also self employed it can be tough but if he works he will have to pay up to look after his family, of course he will.
Would I be entitled to any help?
Almost certainly. But I believe that your goal should be to remain in the family home. If he can't afford to stay there and pay you he has to leave, simple as that.
Would I lose any entitlement to our house if I left?
Do not leave before seeking legal advice, especially do not leave the children with him.
I should imagine that the house would have to be sold when we divorce. If so would that affect any of my percentage of the sale?
I doubt it very much, that is a job for the lawyers and courts though.
Hopefully some more clued up posters will be along shortly to offer advice.
Stay strong.