Yes he does still retain rights to the property so long as you remain marry. In order for your husband to waive his rights to the house, he would need to sign an agreement, sometimes referred to as a post-nuptial agreement where he explicitly waives his rights to the property.
Maybe. If it was signed during the marriage you have the burden of proving it was not done under duress. The community may still have an interest even with a quitclaim.
Generally, a quitclaim deed results in a person relinquishing all rights to the property in question. I recommend you consult with an attorney to discuss your specific situation in greater detail.
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