Changes to latest illustrator

1. a  lasso tool was added which can help with that. I usually for example lock or hide my background layer and then frame select with the direct select tool to get what I need.

2. not sure how rcraighead​ gets shift command 3 to work.  I disabled my conflicting key command for screenshots in system preferences, and was not able to get that.  Would save  a step from what my usage of  select >> inverse  & hide instead.

or set layers to be printable or hide them and use this when printing

3. Yes export selection has been added and bit mapped web formats are available, bit not a .ai format.

4. Nothing new has been added to work specifically on items outside the artboard.

1. Marquee: There is a plug-in from Esko which add two tools to the Direct Select called bX Direct Tool and bX Dust Direct Tool. These tools make selecting with a marquee much more intuitive. I find that nobody uses the Magic Wand tool except me where I work. I have found the Magic Wand to be a very handy tool for selecting objects which have similar characteristics. It's like select same menu but with the  flexibility of a point and click tool.

There is a forum for suggesting features for future versions of Illustrator.

Illustrator Feature Requests

1. Marquee… hasn't changed that I know of. Using "Direct Selection" tool along with "Option" and/or "Cmd" keys is more powerful than a marquee in my opinion. Never even use the marquee in AI.
2. Print selected… With items selected that you want to print, type "Shift-Option-Cmd+3" to hide all unselected and print. You can always save that as an Action if you'd like.
3. Save selected as… You may find the new "Asset Export" and "Export for Screens" features useful for this.
4. print/export/save as anything… Not sure what you're asking here. You want to do something with items outside the artboard? I would select all, then Shift-Option-Cmd+Drag over the artboard to deselect artboard items, then do as you wish with the remaining selection.