No the option to transfer the case to a waiver based one is not required from USCIS.

Yes but you should have DACA approval, EAD and valid passport to travel.

Yes if you are otherwise eligible to participate in DV lottery.

No this should not impact your case other than regarding financial support requirements.

The answer to both is yes based on information provided.

Depends on the nature of the warrant. Consult with a criminal defense attorney for resolution.

No you must notify NVC of changed status as your spouse would no longer be eligible for petition.

Yes this is likely due to Covid backlogs and delays.

Consult with a Mexican immigration attorney for guidance.

Yes it is permissible to do so during the naturalization process.