I believe those are cover caps for the struts - they have access holes to put in a long deep well socket so the shock portion of the strut can be removed from the vehicle and the springs come out with it.. These look to be the plugs for those access holes.- they are in the engine compartment and cover the strut mount.
The running rough - when the age of the vehicle gets up there and little to no maintenance is done - rough operation can mean many things - can you be more specific?
Could be gas, poor connections from or simply a dying or a weak battery - onto fouled plugs onto broken hoses leaking in air into the manifold onto a broken tailpipe gasket onto - ad nauseaum
These fell off my mother in law's 2016 Fusion. No markings other than a 1 and a 3 on the inside. Any idea what they are? Her car started running roughly the same day these were found. Not sure if these things are at all connected. Nothing is leaking or appears broken on the underside. Any help would be greatly appreciated! 🙏