Well, for posterity, I'll answer my own questions as best I can:
Proxy server any port can be set in the OS environment ("http_proxy") and the widget seems to respect this setting.
override QtWebEnginePage.certificateError, which should return true if we're ignoring the error. Unfortunately the widget doesn't actually call this function for a lot of certificate errors, so it's not working right now.
File downloads aren't supported, maybe in 5.5
tl;dr - QtWebEngine is very young, wait for future versions for it to be usable.