This is related to a modification you've made to open navigation menus when hovering over top-level items. Your displayed menu inherits CSS rules that cause the lines not to wrap. The core behavior creates menus dynamically as direct descendants of <body>, which avoids this. You would have to...
It would require an add-on as the order is determined in the templater. If enabling banner stacking is an option, you might be able to work around it by creating an additional user group (and banner) for staff members.
The phrase should be created at the same time the dropdown is (and is present on my local installs), but due to an older bug it may be missing if your installation was created between XF 2.2.0 Beta 1 and XF 2.2.0 Beta 6. Could that be what happened here?
It may be because the image changes the dimensions of the horizontal scroll container after we've already taken measurements of it (to know whether or not to display the arrow). If you add dimensions to the image tag (width="39" height="28" should do the trick), does the issue persist?