Unless the iPad can be restarted to a running state - and you can successfully enter the device Passcode - you will not be able to recover any locally stored data from the iPad. If you have a pre-existing backup of the iPad, this backup can be restored to the replacement iPad.
Your iCloud storage quota is shared by all devices that are signed-in to iCloud with the same AppleID.
In more detail...
Assuming that both the source (old) and target (new) iPad are functional, these support pages should get you started with setup of your new iPad - and the methods of transferring your data from old to new iPad:
Set up your iPhone, iPad or iPod touch – Apple Support
Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support
If the donor iPad, from which you are transferring your data precedes iOS12.4, QuickStart will not be available.
“Transfer” is rather a misnomer. In reality, your data and setup is merely cloned to the new device. Nothing is moved or removed from the original device.
An alternative is to restore either an iCloud or iTunes backup to the new device. This method must be used if the source iPad is not functional, but is contingent upon having a pre-existing backup:
How to back up your iPhone, iPad and iPod touch – Apple Support
Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
Apps are not directly transferred between devices. For Apps, the transfer process creates a record of the Apps that are installed on the donor iPad - and it is this record of installed Apps that is transferred to the target (new) device. For Apps that are still available for download from the App Store, the corresponding Apps are automatically downloaded and installed from the App Store.
If you need assistance, you can make an appointment for the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) here:
Genius Bar Reservation and Apple Support Options - Apple
