After I erase my iPad and give it to someone else, can they download from their iPhone?

Worse case scenario.

You will need to start by backing up your daughter's iPhone to either Apple's iCloud ( you may need to pay for additional, monthly storage space ) or by connecting your iDevice to a computer running the latest iTunes or, if a newer Mac with a much newer macOS, use the macOS Finder to do the device backup and/or some other offsite, “cloud” data storage/backup services, like Google Drive/Photos, BOX, DropBox, Amazon Cloud Drive, Flickr ( for photos/images ), etc.

Then restore that iPad from your daughter's iPhone backup.

Don't worry about how another owner will use and setup this iPad, if yoy plan on giving this iPad away or selling it.

If they have any backups of their iOS devices they can transfer the backups to this iPad,

Here is what YOU need to do to prep that iPad.

What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

As far as apps go, if the apps are recent and NOT too old, the new owners can easily get their own apps from the iOS App Store to download and install, themselves.

You need to completely clear and erase the device per the link I supplied.

Not sure if the Quick Start routine will work, or not, on such an old iPad.

You'll just need to try it.