Do prior-service Marines get the Army Service Ribbon? Is a Sea Service Ribbon to an overseas deployment authorized to be worn in the Army?

You get the Army service ribbon upon completion of AIT when you reclass....its automajic. Also, your sea service ribbon for the corps also crosses over.

Yes you can. Take your dd214 to S1 and any awards you’ve earned. They will be put on your ERB.

Sgt Darren Mattice from HRC
"Soldiers awarded a decoration or badge for service with a Sister service prior to service in the Army need to request wear of that decoration or badge to HRC ADB.

To request to wear Sister service awards, a Soldier must submit a memorandum or DA Form 4187 requesting wear, documentation showing the requirements for the award and certificate and/or citation confirming the requirements were met, and appropriate orders or other official supporting documentation that clearly defines the assignment relationship to the other service to the HRC ADB. If not clearly documented, the recommendation will not be approved for acceptance or wear.

Effective 2 August 1990, a commissioned officer of the U.S. Public Health Service (USPHS) assigned or attached for full-time duty to the DOD or any of its components is eligible for military awards and decorations on the same basis as officers of the military services. However, no military ribbon, medal, or decoration will be awarded to an officer of the USPHS without the approval of the Secretary of Health and Human Services or designee. Requests for concurrence may be obtained from USPHS Commissioned Corps Liaison Office, Office of the Assistant Secretary of Defense (Health Affairs), 1200 Defense Pentagon, Room 3E1070, Washington, DC 20301–1200."

https://www.hrc.army.mil/content/Sister%20Service%20Awards

Army Service Riibbon AR 600-8-22
"5–5. Army Service Ribbon
a. The Army Service Ribbon was established by the SECARMY on 10 April 1981 as announced in DAGO 1990–15. It is awarded to Servicemembers of the U.S. Army for successful completion of initial entry training.
b. Effective 1 August 1981, all members of the Active Army, ARNG, and USAR in an active Reserve status are eligible for this award. The ribbon may be awarded retroactively to those personnel who completed the required training before 1 August 1981 provided they had an Active Army status as defined above on or after 1 August 1981.
c. Officers will be awarded this ribbon upon successful completion of their basic and/or orientation or higher level course. For those officer personnel assigned a specialty, specialty skill identifier (SSI), or MOS based on civilian or other service acquired skills, this ribbon will be awarded upon honorable completion of 4 months active service.
d. Enlisted Soldiers will be awarded this ribbon upon successful completion of their initial MOS producing course. For those enlisted Soldiers assigned a MOS based on civilian or other service- acquired skills, this ribbon will be awarded on honorable completion of 4 months active service.
e. Only one award of the Army Service Ribbon is authorized, regardless of whether a Soldier completes both officer and enlisted initial entry training.
f. An individual may be posthumously awarded (on or after 1 August 1981) the Army Service Ribbon prior to completion of the requisite training or time in service, provided the Soldier’s death is ruled "Line of duty-Yes."...."