The little vector arrow showing up when clicking on a surface is that you have Instant3D on. You can turn it off by clicking that button on the Features Tab of the command manager, or by typing instant3D into the search box and click on the icon next to the name that shows up in the results.
The tree at the top left is the selection breadcrumbs. If you don't want those, you can find the setting in Tools > Options > Display or just search for "breadcrumb" in the system options dialog.
It depends. If I click with the left mouse button then shift the mouse over a bit the click and release the wheel, I see the first image with the dotted line. However, if I click with the left mouse button then hold the wheel button down, I see the second one. The second allows me to rotate the view angle.
The vector arrow and tree options advise helped me remove these. Thank you. I was hoping this may have something to do with the main issue I am having, but after making these changes I am still having the issue of not being able to rotate the view angle without these extra steps.
Thanks for the help!
A colleague of mine just informed me of a change that occurred in the settings last week. Hopefully this will help anyone else who is having this issue. To fix this problem, I had to go to the 'Add-Ins' menu and uncheck the two boxes next to 'SOLIDWORKS Forum 2017'. After exiting and restarting, this issue was resolved.