Yes, but flying within the gliding distance of emergency airports is acceptable (unless of course there is an emergency during early stages of climb or late stages of descent).
Nope. ETOPS allows planes to operate up to 180 minutes away from an emergency landing field, almost 10x the world-record glide distance quoted in this article.
Multi-engine failures on a twin engine aircraft are the rarest of the rare events and so far there have been less than a handful such events in record and as such, in my comment I assumed that gliding would imply a single engine failure as is implied by ETOPS which you failed to note.
The quoted flight as a result of a massive fuel leak and ignorance on the captain's part to notice fuel imbalance led to dual engine failure.
Also, ETOPS itself has multiple ratings and the A330-200 (in the quoted flight) was certified for ETOPS120 or 120 minutes away from an emergency field on the flight plan and not 180. The new 300+ series rated with ETOPS180 and beyond have a higher composite content to reduce weight and perhaps more fuel efficient engines (ETOPS implies single engine failure).
This being a post about airliners crossing oceans, and ETOPS being thrown about - you'd expect people would know.
Without any power, airliners can't really glide much. Of the few cases of all-out engine failures, even fewer make it safely to land or water - most of which that did were at their cruising altitude at the time of failure. With only memorable exception being the hudson river ditch.
In-fact, during the landing or take-off, even a single engine failure can catch the crew off guard and is among the worst case scenarios pilots are "trained" for.
https://en.wikipedia.org/wiki/Air_Transat_Flight_236