this is critical, you nee to find out what the construction is. Once you see it you'll soon see what's wrong & realise how straightforward to repair it probably is.
I certainly would not assume that.
If the floor is sagging in the centre, the problem is more likely supports that are sinking or rotting, or rotting joists.
most floors aren't, but we have no way to kmow. You will once you take a look.
probably.
there are multiple options. Start with knowing the existing construction.
sure, long as it's not glued down or foam backed.
Lift a corner of carpet, lift a sheet or board & tell us how it's constructed. You won't make much progress by any other means. And tell us where the gaps are where one bit isn't supporting the bit above.