Some suggestions about dragging from Adam C.:
"If I might suggest, if dragging isn't possible, why not just make it that when you select an image, you have a few buttons. A left arrow to move it left, a right arrow to move it right, a menu button between them that'll give you the chance to edit image properties (and to set the rarely-used centre), ideally a way to directly edit the caption without entering a menu, and perhaps a little drag bar at the top for moving it vertically? (Having a standardised place to grab and drag would be an excellent idea, by the way.I'd suggest adding a little bar at the top of an element when it's clicked on.)".

fwiw about Problem 1 the same happens with text based templates. Tested with the template {{languages}} at the top of the page at https://www.mediawiki.org/wiki/Groups

This doesn't appear to be a problem in master.

Specifically, this was fixed by Ed's changes to clickable nodes last week.