1) When the mouse is moved quickly below the tabs the territory name linger until the mouse is moved above the tabs. This might be attributable to my slow old computer.

2) Text is highlighted when the mouse is dragged from an undraggable black area or when a window is dragged when there is a undraggable black area under the point where the mouse starts dragging.

3) Tab buttons and buttons on other windows can be activated through the draggable area of a window and through every part of any upgrade window except through the buttons.

4) "Dig Started" balloon does not close automatically and cannot be set to auto close in the app settings. Balloon stays in the same spot when the browser window width is changed.

5) Windows always open covering the tabs. I rarely open a window without moving it. It would be nice if the windows opened where they were when they last were closed.

6) Animations run slow on older computers. A choice of which animations should be active would be nice. I could do without all the window and tab related animations.

7) Changing the width of the browser window with a game area narrower than any open window will also change the width of the open window.

For the recipe stats window (granted by statistics level 3):

8) Column widths can be changed by dragging the column header from a point on or close to the border to the next column and then releasing the mouse button when the curser changes to "forbidden". After that moving the mouse will change the width of that column and other columns. If the column becomes very wide the columns will expand outside the window!!!

9) There are no visible arrows indicating that the columns can be sorted but they can be used anyway. Only after the first time a column is sorted an arrow is shown.

I get annoyed by 1, 2, & 4 all the time.

Not sure what you mean with 3.

5 would be nice.

6, A lot of the animation on PC can be turned off. Just did this in the last week.

7, never dealt with this, but if I ever maximize my browser and have my artifact window open, the artifact window expanse from top to bottom of the page.

8, I haven't dealt with this either, but I check and it does happen.

9, this is because its sorted in the order you get the recipes when you first open it up, which means it isn't sorted by any of the columns, so there should be an arrow on any of them. Makes sense to me.

Not sure what you mean with 3.

Open any upgrade window (army camp, hospital, or mine).
Move the upgrade window so that it covers any button in the tabs.
Move the mouse to the area of the upgrade window that covers the button.
You will notice the mouse pointer will change from an arrow to a hand.
Now when you click on the upgrade window the button covered by the upgrade window is activated.

6) Changing from one tab to another will activate a slide animation, sliding the old tab out and the new tab in.
Opening or closing a window will activate a zoom animation of the window from small window to full window or full window to small window.
These animations cannot be turned off afaik.
In mid to late game on big maps my old computer already struggles when I drag the map around, so animations just add unneccesary workload.

7) Yup, thats about the "size" of it. You can make the browser window so narrow that the open window eg artifact window starts getting narrower which is when the artifact window is"attached" to the browser window and follows the width of the browser window.

9) It is not a given that a column in any table can be sorted. So a visual clue is needed, namely an arrow.

I wonder if these issues are considered bugs and should be reported as such?

If I understand it correctly #3 is the worst. I went to the end of the mine list to select all the diggable locations and tried to activate a 4 billion dig site but the purchase button from the dig window overlapped with the upgrade button of my last mine which was for 8 billion or so. Needless to say I was not amused when I ran out of money when my click was accepted by the mine upgrade button instead of the thing I clicked which was the dig buy button.

It also happened a few times with territories iirc.

Either use Help > Contact > report bug or go to https://www.warzone.com/ReportBug and provide the required details. the more precise the details are, the easier the bug will be to recreate and therefore the faster the bug can be to fix

6, A lot of the animation on PC can be turned off. Just did this in the last week.

How??
I have a decent PC but the lag makes it really hard to play Idle. (I am also sure there some computer or browser settings I can optimize outside of the game itself but I have no idea how to do that)

How??

While in idle, click on your account name in the top right, then click "App Settings" and deselect whatever you want to prevent from coming up. Unfortunately, you have to do this each time you log in (or this might be a cookie thing, given that cookies don't live for long on my system).

Use Help > Contact > Report Bug