1. Not following you here. Where did you find a cut polygon option?
2. Yes, creating your own tool will work fine. Just remember a tool will belong to the current style, the tool won't automatically be available in other map styles unless you manually load the tools from another style.

Joe is right about the resolution mode here.

What happens here is that CC3+ keeps each image in four different resolutions, so it only shows the resolution needed based on your zoom level for faster operation.

However, those affected trees of yours are not the same size as the rest of the trees, they're about 10% smaller. This means that when you zoom out, they switch over to lower resolution versions a bit earlier than the others, and if you hit just the right spot when zooming out, those trees have switched over to the lower resolution version, while the others have not.

You can fix this as Joe points out by using :CC2RESMODE: and forcing them to always display very high. This may not be a good idea for a big complicated map, but for this small map the performance difference should be minimal.

This shouldn't affect image exports, unless you export it at rather low quality, in which case the same can happen for the same reason, with the solution being the same.

Which sheet is that? You cannot hide the the sheet CC3+ wants to place the symbols on. For example, most regular symbols goes to the SYMBOLS sheet, so that will be unhidden whenever you pick a symbol from the symbol catalog (but the screen isn't immediately redrawn, so it won't be visible until you do an action that redraws the screen, such as zooming in/out)

If this is what's happening for you, you can handle it in two ways. Either turn off the option "Symbols choose their own sheet" from the options button in the symbol catalog, OR make sure your current sheet is named something that starts with the word SYMBOLS since CC3+ will then use that instead of the main SYMBOLS sheet.

(Note that some special symbols defaults to another sheet than SYMBOLS, they would show the same behavior with whatever sheet they were set to go on)

An interesting battle map indeed :)

I'll go for the DD's.