Would a hint be negotiable?

Sure. There is a bottle of alcohol and a Lincoln relative involved.

HA - Peggy Lincoln Beckwith and Robert baptized the sub! ("The Last Lincolns")

Got it! Although I'm not sure Robert was there. Was he? Anyway- this was fun!

What ship (specifically as for the forum topics) is depicted here?
   

Wild guess - the Thomas A. Scott? (Dr. Mudd tried to escape from Ft. Jefferson)

This is an outstanding guess, Roger, but sorry, not correct!

Hint #1: I will answer yes/no- questions.

Does it have to do with Mary Lincoln in any way?

Was this photo taken after the Civil War?

Two excellent questions, Roger and Gene - no to both!

The Trent?

Looks like a troop transport ship.
Looks like it is undergoing some repair/modifications.
Shape is similar to the Sultana, except for the paddle wheel.

A very good idea, Roger, sorry, not the "Trent" either. (I really think this is a good question btw!)

Hint #2: Please think about hint #1and try to narrow it down!

Good ideas, Gene! This ship certainly had never been used for troop transport, but similar shape to theSultania is "hot" - not the Sultania, but indeed similar vessel.

Was Abraham Lincoln ever aboard the ship?