Yes.
Although it’s not strictly necessary, “zypper up” should work as well (except if there are package downgrades, which should rather be the exception than the rule though).
“zypper patch” will not do anything though, as the main repo is rolling until the release, there are no updates in the Update repo.
After using zypper dup I’m not getting any updates anymore (and since this is beta, I expect a lot of them).
Well, if you are fully up-to-date, there are no updates of course.
The development model is similar to Tumbleweed. Updates are tested, and if all tests pass, a new snapshot will be published.
So it’s to be expected to get updates only every couple of days… (maybe once a day)
Trying zypper dup or zypper up I also get this message:
Repository 'openSUSE-Leap-15.0-Update' appears to be outdated. Consider using a different mirror or server.
See above, there are no updates, the repo is empty, and that causes this message.
When I use network share (via secondary Wifi adapter) and logged in Wayland session, after my screen goes to sleep (or rather gets locked after 5 min) not only do I lose the shared wifi connection, but I’m not able to wake up the screen again. Did not happen with X.
Then use X instead? 
Wayland is still somehow experimental.
Also how can I submit a request to include a package and/or upgrade a package that is already in Leap 15 repo?
Submit them on OBS.
But a package has to be in Factory first before it can be submitted to Leap.
Submissions to Factory should still get forwarded to Leap 15 automatically by the bot at the moment.
(new packages probably not, but I’m not sure)
Although you can also submit to Leap 15 manually. (but again, changes have to be in Factory first)