QDRO in unsigned separation agreement

Based on all that I’ve read, it is my understanding that if a separation agreement is unsigned that the QDRO for 401k accounts is unenforceable. If the agreement is not signed and there is no claim for ED when an absolute divorce is granted, then the spouse cannot make a claim for the 401k amount they wanted? Can you confirm?

Also, if the spouse was perfectly able to work and chose not to, would a judge automatically grant that they get 50% of the assets? Bascially we said in our unsigned agreement that to make up for my 401k having more value than his, that I would give him part of my 401k to make it even. Now I’m wondering if I should do that based on the fact that he should’ve been working all these years and if he had been, his 401k would be closer in value to mine. What are the general rules on a non-contributing spouse?

If a spouse does not work for several years and does not bring in income, causing the couple to refinance and live off of savings and equity in the home, is this considered marital fault?

That is correct. If there is no signed agreement and no pending claim for equitable distribution at the time of divorce the retirement account will not be divided.
A judge does not automatically grant a 50% distribution of assets. He or she must hear all evidence, and consider any factors regarding an unequal distribution of property if either party made a claim for an unequal distribution.
A non-working spouse is usually not considered to be at fault economically speaking.