Can I file a DS-260 while fulfilling the J1 waiver requirements?

Yes, you can. However, the filing may not necessarily speed up your application for an immigrant visa as the NVC will not approve the DS-260, until the NVC considered your filing to be documentarily certified, meaning there won''t be any real processing until all required documents are turned over to the agency. In fact, you may receive a few documents requests for your application. If your waiver were to lag behind, your application will not be certified for an interview. Advisably, make sure all steps are taken that your plan is precisely planned and your idea does not lead to immense delay.

Yes, you can proceed with I-526 processing while you are fulfilling your J-1 requirements.

I believe you can only file an I-485 while fulfilling the requirements and this will allow work and travel permits but will not be adjudicated until your requirements have been fulfilled.

Ideally, you should not schedule the interview until the waiver has been granted.

Yes, you can file the DS-260 while fulfilling the two-year home residency requirement as a physician in an underserved area. It might be easier to file an adjustment in the U.S., however.