How much equity of my house is my ex entitled to?

Yes, your spouse has a claim to that equity which acquired during your marriage. In Nevada, that fact that you separated is entirely irrelevant the community continued, and your spouse continued to gain an interest in the home despite your separation. There is a very complex formula used to determine the community's interest, which can be found in the Malmquist decision from the Nevada Supreme Court. You really should consult with an attorney as there may be ways to balance other assets and debts so as to avoid dealing with the house.

Maybe. The questions have to do with who paid what, from what sources, before and during the marriage. Separation may (or may not) be relevant, due to some interesting language in the controlling case, Malmquist. For background, see http://willicklawgroup.com/property-rights-and-division/, but you are really going to want to discuss this with a family law specialist well versed in such matters and calculations.