Wasp11b

As regards (3), I find that if a click the row header arrow and select 'Insert Row', it does indeed add the new row above. However, if I ignore the header arrow and just right click on the row header the same menu pops up but this time if you select 'Insert Row' it inserts below the currently selected row! Of course, the operation should be clearly labelled as to whether inserting above or below.

Assuming you don't have Photo and Designer installed (if you do you just need to use StudioLink to access a whole variety of pixel tools including brushes), you could create a mask as follows:
(1) use pen tool to draw the area you wish to retain in the photo or just use a shape tool eg Rectanguar Tool. This will give a new layer.
(2) fill with black, white or any other colour (doesn't seem to make a difference  - a bug?)
(3) right click and select 'mask to below'. Only the photo included within the shape will be revealed.
(4) you can adjust the mask by right clicking, selecting 'edit mask' and then use node tools to amend nodes. Best to do this by releasing the mask so that the photo layer is also revealed and then remasking.
(5) you can also move the mask around, just select the mast layer and use the move tool.
 

"But that assumes manually assigning an A master to every left page, and a B master to every right page, correct?"
If I set up two single page masters for left and right facing pages, as I think was suggested earlier, and apply whatever margins are required (unlink 'edit all margins together'), then if you right click on either master there is a list where there is an option 'apply Master to pages...' where it allows a master to be assigned to all odd or even pages, or indeed specified pages, so you don't have to go through your document manually assigning a master to each page. Does this do what you want?
Interestingly, if you then look at the spread setup properties for a page assigned left or right masters, the margins do not reflect what is on the master page, although they seem to be displayed correctly on the page. Must be a bug, I suppose.

I find that a discontiguous selection on the page can be made by just shift clicking each item. The bounding box may appear to select more items but after shift-clicking whatever items you want, you can copy and then paste to the page you want. Note - you can also select from the layers panel - here Ctrl-click selects discontiguous items.
Alternatively, you can zoom out (Ctrl-wheel) after selecting and then move your selection to the pasteboard ie off the page. You can then select an item or items on the pasteboard and move them directly to a page in zoomed out view or right click and cut or copy (or use the Layers panel) and then on the Pages panel select the page you want by double-clicking and then paste. 
Works for me on Windows. May be a better way of implementing but hope that helps.