The short battery life is inevitably due to the iPad's age. Rechargeable batteries are a consumable item - that sooner or later will need to be replaced to restore normal performance. A rapid drop in reported battery charge is a reliable indicator of the battery nearing the end of its useful lifespan. An iPad battery is rated to retain 80% of its original capacity (when new) after 1000 charge cycles; every full charge cycle reduces the capacity of the battery by a tiny amount, this degradation being cumulative.
For the time being, using your iPad while it is connected to its Power Adapter will allow you to use the iPad normally. However, if [when] the battery completely dies, the iPad will be unusable.
Moving on to the Passcode being required instead of TouchID... As documented by Apple in its Security Guide, for devices with TouchID or FaceID enabled, your device Passcode is always required in the following circumstances…
A passcode or password is also required if the device is in any of the following states:
• The device has just been turned on or restarted
• The user has logged out of their Mac account (or hasn’t yet logged in).
• The user hasn’t unlocked their device for more than 48 hours.
• The user hasn’t used their passcode or password to unlock their device for 156 hours (six and a half days), and the user hasn’t used a biometric to unlock their device in
4 hours.
• The device has received a remote lock command
• The user exited power off / Emergency SOS by pressing and holding either volume button and the Sleep/Wake button simultaneously for 2 seconds and then pressing Cancel.
• There were five unsuccessful biometric match attempts (though for usability, the device might offer entering a passcode or password instead of using biometrics after a smaller number of failures).
When Face ID with a mask is enabled on an iPhone, it’s available for the next 6.5 hours after one of the following user actions:
• Successful Face ID match attempt (with or without a mask)
• Device passcode validation
• Device unlock with Apple Watch
Any of these actions extends the period by an additional 6.5 hours when performed.
As for your Home Screen layout, this will be reset along with other device settings when you perform a reset.