Hi and welcome!
In AmiKit, you should be able to select exactly the same screenmodes as you use on your PC. Run the "AmiKit:Prefs/ScreenMode" program and check it out. If the particular mode is there, don't do anything. Let's adjust AmiKit graphics and windows sizes to the high resolution first. Run the following program:
Select the screen mode that is closest to the one you want to use. In this case it's 1680X1050. Then press the Apply button. On next request press the "Visible" button.
Then the program encourages you to set the real screen mode in your system prefs too. So press the "Run Screenmode" button and select the exact mode there: UAE 1920x1080 32bit BGRA and press the "SAVE" button.
Regarding the theme, you can use MorpheuZ program (located on desktop) to change the appearance of windows graphics. Select the one you like from variety of classic or 24bit themes.
You can also change the desktop background. Simply press right mouse button over the image file and select "Set as Background" item. For more possibilities, left click the desktop (so it is activated), then press right mouse button and select "Settings -> Environment" item.
Regarding your last question, yes, AmiKit is compatible with the most AmigaOS3.x programs. MANY of them are already included. Check out the start menu, for example. AmiKit is not compatible with AmigaOS4.x programs, though, as that's completely different architecture.