In the browser's private storage on the device you opened them on. When you open a file, Model Explorer converts it, usually to glTF, and keeps that copy with a thumbnail, and each model gets a card on Home on 0xr.space. Nothing is uploaded and nothing syncs, even with an account, which holds only your share links: the models on your phone are not on your Quest, and those in one browser are not in another.
The browser owns that storage. Clearing site data for 0xr.space deletes every model, a private window cannot keep them, and since the site does not ask for persistent storage the browser may clear it when the device runs short of space. When it is full, an import fails with Device storage is full, or this browser’s storage quota was exceeded. Keep your original files. A stored model can be downloaded again as GLB, STL or USDZ from its card's three-dot menu with a free account, but that is a converted copy, not the file you opened.
Share one to make a link and open it on the other device. That uploads it, and the link lasts 30 days. Otherwise copy the original file across.
No. A link you made keeps working until it expires 30 days after upload.
As much as the browser allows the site, which depends on the device's free space. Settings shows how many models are stored.
Yes, with a free account. Once the model is open it has a card on Home: open the card's three-dot menu and choose Download GLB, Download STL or Download USDZ, then sign in with the 6-digit code sent to your email. The STL is binary, in millimetres with Z up and no colour; the USDZ is for AR Quick Look on iPhone, iPad and Vision Pro. Splats, point clouds and gallery models with a limited licence cannot be downloaded.