Does it work on the same office network without internet?

Not yet. Both sides need an internet connection to reach the servers; a LAN-only mode is on the list.

Will the company proxy break it?

An HTTPS proxy that allows WebSocket connections is fine. A proxy that inspects and rewrites TLS will stop the session from connecting; ask the administrator to allow acrossview.com through it.

Is a relay a security risk?

No. The relay sees encrypted packets it has no key for. The keys are made on the two devices during the handshake, and the six-digit security code on both screens shows no third party took part in it.

Remote support without a VPN or port forwarding

How two computers find each other

Both sides make an outgoing connection to AcrossView's servers in Mumbai, the same way a browser opens any website. Outgoing connections work through nearly every firewall and router, so neither side needs to open anything. The servers introduce the two computers to each other; after that they talk directly when they can (most home and office networks), and through a relay in Mumbai when they cannot (strict corporate firewalls, some mobile networks).

Either way the session is end-to-end encrypted: the relay carries data it cannot read. See Security.

What a network administrator needs to allow

HTTPS (port 443) to acrossview.com and its subdomains, for the pages and signalling.
UDP to the relay on port 3478 gives the smoothest picture; if UDP is blocked, the session falls back to TCP on 443, which still works.
No inbound rules, no port forwarding, no fixed IP addresses on your side.

Where it differs from Windows Remote Desktop (RDP)

RDP shows you a separate session and locks the person out; AcrossView shows the screen they are looking at, so you can work together and they see everything you do.
RDP needs Windows Pro on the far side and a route to it; AcrossView needs a browser (to view) or the free app (to control), on any edition of Windows.
RDP exposed to the internet is a favourite target for attackers. AcrossView's app listens on nothing; it only makes outgoing connections, and each session needs a press of Allow or an unattended-access password.

Mobile data and hotspots

Jio, Airtel and Vi connections put phones behind carrier-grade NAT, which breaks anything that needs an inbound connection. AcrossView is fine with it: the person being helped can be on a laptop tethered to a phone, and the helper can be on mobile data too. On a slow link the picture drops frames rather than sharpness, so text stays readable.