Can I buy a house and take on a mortgage while my divorce is pending?

The Restraining Order prohibits you from transferring, hypothecating, etc. community or separate property without written consent of other party or court order except for necessities of life. Any reason why your soon to be ex won't give written consent? If she will, problem solved. If she won't, safe thing to do is get court approval.

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Unless you want to make your (and your co-buyer's) life more complicated than it needs to be, you should either

wait until your dissolution is final (when you say you're "waiting for the judge to declare the settlement final", has a JUDGMENT been entered yet?)

OR

get a separate agreement and order signed by your (soon-to-be, but not-yet) ex-wife to the effect that you are not using any community property to buy the house, you are not relying on her credit in any fashion to buy the house, her name will not be on any loan to buy the house, and she's waiving any claim that there is any community property interest of any sort in the new house

AND your escrow company will want a quitclaim deed from her as well.