Pair two phones with a QR scan, then transfer directly over Wi‑Fi at MB/s. No cloud, no app.
No. Wi-Fi Beam is a direct WebRTC connection between the two devices, encrypted end to end with DTLS. Most browser transfer tools still use a signalling server to introduce the two peers to each other; Beam does not — the pairing details travel in the QR code you scan off the other phone's screen, so there is no server in the loop at any point.
They need to be on the same network, but that network needs no internet at all. A home Wi-Fi with the router unplugged from the modem works, and so does one phone's Personal Hotspot with the other joined to it even on a plan with no data left.
There is no imposed limit, because nothing is uploaded. Wi-Fi Beam runs at megabytes per second, so full-length videos are reasonable — the practical limit is your patience and the receiving phone's free storage.
A room name has to be coordinated somewhere, which means a server. Scanning a code off the other screen proves the two phones are physically together and carries the whole connection offer in about 85 bytes, so the pairing needs no third party.
Almost always the two phones are not actually on the same network: one is on Wi-Fi and the other dropped to mobile data, or they are on a guest network that isolates clients from each other. Hotel and corporate Wi-Fi very often block device-to-device traffic on purpose. Use one phone's hotspot instead, or switch to QR or Sound mode.