Yes, that Republic FO could bid to a new 175 domicile at Republic. As for base downsizing, an FO has to stay on equipment type (135/140/145, 170/175/190/195, or CRJ) as long as there are positions elsewhere in the system and pilots junior to him/her. If you are most junior pilot on the equipment system wide, then you would be displaced to another aircraft. So an SDF CRJ FO who gets displaced due to downsizing would have to go another CRJ base, and cannot bid to be a 145 FO in SDF.

As for reserve in DCA, I do not know how long it is currently running. But the Republic fleet is growing from 28 to 58 aircraft in the next year and a half, so overall your time on reserve should not be more than a few months. Who knows if DCA will stay junior if and when new domiciles are announced.