The first one is indeed an EK. It looks vintage maybe even WWII. This one might be worth a fair bit of money, so dont part with it and certainly dont restore it before others chime in. The 'rivets' are soft and meant to be pounded on further, should the handle slabs loosen up and move about.
The 'rivets' should be easily replaced - I'd advise to not touch the wooden handle slabs, unless they are Falling apart and cant be held together by replacing any lost 'rivets.'
The EK looks great and seems to have seen some action. A rugged knife, which has been used - I would be porud to own a similar knife.
Make sure you get a second opinion and get the knife valued correctly before parting with it.
The other knives looks like Fairbairn-Sykes clones.