Technically that Beneficiary may travel with a valid visa as intended but discuss all details with a licensed counsel prior to the planned...

You have no criminal history as there was no arrest, charges, processing, detention, fingerprinting and custodial detention. Zero impact.

List the full legal description of the place of birth with both words.

You may use the new name on a federal form recognized by the U.S. Department of State as that present country.

You must immediately discuss your best legal options with a licensed family law attorney. It would be much cheaper that a possible financial ruin.

Your foreign national spouse may remain in the U.S. pending the final decision on his adjustment of status to LPR in the United States.

You must contact the Swedish authorities to reissue the son's passport and then seek an emergency B-2 visa from the local U.S. Consular Visa...

You may discuss your exact legal plan prior to your departure with a licensed immigration professional directly.

That description should not disrupt your immigration case at all.

You will create a considerable legal mess acting without a licensed attorney versed in that area of law.