When to use Family Sharing and when to create separate AppleIDs

I would recommend that you each have your own Apple ID. With all of the things that can be synced via iCloud, sharing an Apple ID can cause a number of issues of data from one phone syncing to the other or deletions on one phone syncing to the other.

Family Sharing works with different Apple IDs. If you use the same Apple ID, then you render family sharing completely moot. As an Apple ID already has access to all its content and purchases and content regardless of device.

Anyway, each person should have their own Apple ID.

While the Apple ID is tied to the email, unless its an iCloud Email address, it is not in any way tied to its password. Changing the password for the email account will not affect the password for the actual Apple ID, again unless its an email address. If its a 3rd party email account, she can change the email password as much as she wants and it will not affect the Apple ID password.

Also, the Apple ID password in general will not be required on a regular basis on an iPhone, so she should not need to remember it.

There’s also the option of you having the password, and telling it to her if she forgets it, should she need it.

The only real place you would need to enter the Apple ID password normally is when downloading items from the iTunes and App stores, and you can set that to not be required.

Yes. With Family Sharing you can search for devices in the family group.

See here: Share your location with your family - Apple Support

Has she tried writing down her ID and password and keeping that in a familiar place?