I've been thinking about these, so will jump in again and hopefully prompt some others into offering ideas. We inherited a lot of non-beekeeping woodware, a lot of it had to be thrown away because although it looked okay it hadn't stored well and wasn't worth repairing.
Some of your brood boxes (the deep ones) are nailed. The nails could have rusted and, if they break when you lift the boxes you might find yourself holding a couple of pieces of wood, a mess of hive contents at your feet and confused bees all round your head. So I'd check, and glue and re-nail as and where needed before even trying to use them.
Can check that the wood is sound? It may have been damaged by woodworm (if you have woodworm) or other wood-boring insects. You can't really use an insecticide to treat it, because you'd risk harming bees you put in the boxes. If the wood is damaged it could break or crumble when put under stress.
Maybe somebody else knows what the boxes in picture #2 are