How do I get the screen to be dark with white letters? I have the "display and brightness" control on "dark", but some apps like kindle are still white screen and black letters.

Please try going to Settings > Accessibility. Then scroll down to Display and Text Size, then Smart Invert. I just tested it and it seems to do what you want. There are other features you may want to try out.

To answer your second question, you can take a screen shot by pressing by following the instructions in the link below:

Take a screenshot on iPad - Apple Support

Be aware that support for Dark Mode must be coded by the App Developer. As such, not all Apps will necessarily support Dark Mode.

For Screenshots, see the iPad User Guide:

Take a screenshot on iPad - Apple Support

In addition to using physical buttons, you can trigger a Screenshot with finger using a corner-swipe gesture.

iPadOS 16 and earlier

Settings > General > Gestures > 

• Allow Finger Swipe From Corner - set to ON
• Left Corner Swipe > select Screenshot or Quick Note as required
• Right Corner Swipe > select Screenshot or Quick Note as required

iPadOS 17/18

Settings > Multitasking & Gestures >

• Swipe Finger from Corner - set to ON
• Bottom Left Corner > select Screenshot or Quick Note as required
• Bottom Right Corner > select Screenshot or Quick Note as required