As of auto complete, few people have reported issues. In our testing we did not run into this issue. Right now we have an issue and a reproducible test case to tackle this issue: https://github.com/browserhtml/browserhtml/issues/1157
Feel flee to report more browser.html issues here: https://github.com/browserhtml/browserhtml
We'll do our best to get them resolved promptly.
Anyway, what it is doing right now is seeing "http:/" and thinking <Ok, I can just add /sitethatobviouslyhasnorelevanceyet.com and everything will be fine!>. But while it was thinking, I already started typing the second "/" and didn't notice so I got in "lo" before I saw the result. At that point what's in the field is "http:///sitethatobviouslyhasnorelevanceyet.comlo". The issues here are serious enough but it's not entirely surprising you can't reproduce them well.
Edit: Additionally, it doesn't yet support native keybindings like Command left-right or Alt left-right.