I need some advice on how to remove these metal pieces and what I should replace them with. The problem with the metal is it's very loud when I step on it and are so thick they're a tripping hazard. The replacement needs to be secured somehow, and shouldn't bang around when I walk on it.
Can think of a few ways, depending on what you prefer and how destructive you can be:
Use some pressure-treated lumber and create an insert piece that fits into that hole, with some carefully-placed and precisely-cut legs that let it sit on the structure below but flush with the level of the concrete.
This is relatively cheap and non-destructive, just requiring some basic tools.
These are tiles that have a drainage channel underneath, and usually interlock. Lots of styles to pick, and they're not permanent. Downside: They're more expensive and raise the floor level.
You'd just have to be sure that they can span over that hole, or have to add some kind of support structure (eg: pressure treated wood legs).
IMHO, this is probably the best option.
I assume those are paver stones that can be removed, and I can't tell the height of that metal handle but as long as it isn't flush you could replace the two pavers. You'd likely need to route out a spot underneath for that handle to fit into, which would not be a fun job, but the result would be seamless, assuming you can find the same pavers you currently have.
Cut a lip so you can fit a cover (like what you currently have) flush with the floor.
This would require a concrete saw, and is obviously destructive and can't be undone. I'll also put a blanket warning here that this is a potentially dangerous thing to do -- both in terms of modifying something that may be structurally significant, and making a mistake with a saw or modification like this could be catastrophic.
Without knowing what those cover (what you show appears to be unlikely to be permanently coverable), it's hard to give good suggestions. Especially given that it looks like something you shouldn't be making permanent modifications to. Personally, based on what I see, your best bet may be to simply get a hard rubber mat the same thickness as the metal plates, and cut holes for the metal plates.
