Not sure on the first one. I’ve only had that happen on certain clients, but the fact that it happens in the web UI throws me for a loop. Have you dug into the logs when it happens? Looks like there is a debug option you can set in config. I’m assuming you don’t use tailscale to connect while on LAN? When troubleshooting I usually try to eliminate things one at a time. Disconnect from tailscale to eliminate that possibility, connect via IP instead of hostname to eliminate reverse proxy from the situation and see if it improves, etc.
Regarding out and about, what is your upload speed? Are you using direct play or are you transcoding?
Not sure why people are saying port forwarding is required. I have no ports forwarded to slskd and people are downloading from me just fine.