I don't know if it'll work to replace the display rack, but like @LaBlue0314 said sometimes objects stop working for whatever reason when moving to a new lot so it's worth a try! :)
Also, for your second question, I don't have Cats & Dogs, but maybe that lot is bugged or perhaps the tiles aren't all flat? I've heard if you go into lots that aren't flat from Manage Worlds before placing a house there and build a pool across the entire lot, that'll flatten the lot. Just delete the pool afterwards and place your house. Since you've already moved to the lot though, do you have a copy of the house in your library?
If not, save a copy of it in your library, bulldoze the lot, place the pool, delete the pool and place your house again. Hopefully this helps. Also, yes, all elements provide the Focused mood when enabled.
