Mirror iPad Pro to MacBook Air
If you connect your iPad to your computer, you can natively display and record the iPad's screen on the Mac, answering both your questions at once, if I understand you correctly.


Connect the iPad to the computer and open QuickTime Player.
Select File > New Movie Recording (⌥⌘N)
Click the dropdown arrow to the right of the record button and select your iPad's name from the list. (see below—“Seagull” is the name of mine)
If you want to record the screen, simply press the record button.