1.-About the ZIP/UNZIP issue,
in previous versions of Moodle (some time ago) ZIP support was only allowed for *X machines and this worked invoking an external (shell) zip program. Currently zip support in built in Moodle for ALL platforms and leaving that fields empty you'll use it.
And after tons of tests it's really the more reliable method to run backup/restore because it handles complex structures (and backups can become to complex!!
2.-About the BROWSERS issue,
there are some internal timeouts in some of them affecting long tasks. The first timeout is the "inactivity" one. Some browsers, after some "idle" period (without receiving data from the server) close the connection. This timeout has been solved inside the backup/restore utility forcing it to send data to the browser (blank lines and spaces) continuously.
The second "timeout" is the "maxtime" one. Some browsers close the connection after some (fixed) time. This avoid some long restores to be completed. And we cannot do anything here !! It's a browser limitation.
After testing a lot of browsers in some platforms, we have concluded that Konkeror based browsers and IExplorer are more "sensible" to this timeouts, while Mozilla based browsers seem to work fine.
Hope this helps to clarify possible problems in the backup/restore utility.
Ciao, Eloy