Are these sites part of Leumas?

No. Every one of them is somebody else's, run under their own rules. They are listed because they are where the answer to "which version do I own" and "is this homebrew still around" actually lives.

Which file formats does the deck accept?

Each console page says which core runs it and what that core expects. In general: a cartridge dump for the cartridge systems, a disc image for the disc systems, and a compressed archive of either.

Can I search from inside the deck?

Yes. The library screen carries the same directory and searches it in place, then opens the result in a new tab. It still hands you nothing — the file comes from them, the play comes from you.

Where to find games you already own

Leumas hosts no game files and links to none. What it can do is say where to look: the archives that preserve the classic catalogues, the libraries of homebrew whose makers give their work away, and the databases that tell you exactly which version you have. Every link below leaves Leumas, and the search box opens the chosen archive's own search in a new tab.

What is yours to take

A copy of a game you already own — dumped from your own cartridge or ripped from your own disc — and anything its makers release for free, which is most of what the homebrew libraries hold: new games written for old hardware, public-domain titles, fan translations offered as patches. Everything else belongs to somebody, and the deck is built for what is yours.

How the deck fits in

Whatever you find, the deck plays: upload it to your own library and it runs in the browser for the systems a browser can handle, or in the Windows build for the rest. Signed in, the library screen searches the same archives from inside the deck and opens the result in a new tab the same way.

Why nothing passes through Leumas

It is the shape of the product, not a caveat. A console site that supplied games would be taken down and would deserve to be; one that supplies a place to play the games you own can be trusted with your library. The search box here fetches nothing, shows no results and keeps no record.

Questions

Are these sites part of Leumas?: No. Every one of them is somebody else's, run under their own rules. They are listed because they are where the answer to "which version do I own" and "is this homebrew still around" actually lives.
Which file formats does the deck accept?: Each console page says which core runs it and what that core expects. In general: a cartridge dump for the cartridge systems, a disc image for the disc systems, and a compressed archive of either.
Can I search from inside the deck?: Yes. The library screen carries the same directory and searches it in place, then opens the result in a new tab. It still hands you nothing — the file comes from them, the play comes from you.