common law divorce

CA doesn't recognize comon law. Texas does, they suggest people file with the court clerk to have their union legally recognized but if you don't, it can be considered a common law if you meet three requirements.

1) both of you agree you were "married"
2) you must have represented yourselves as married in public, introduced each other as "husband or wife", or filed joint tax returns as such
3) lived together

Be advised, since you own a home and live it in TX, that is where you are a resident so its laws apply.

As far as the house, yes, he can - it is a "marital" asset - and even if you split with him he has up to two years to go to court against you regarding any assets/debts the two of you shared and his entitlements to them if the two of you can't come to an agreement on your own.

I'd see an attorney if I were you.