Crowns and anything purchased from the crown store are available to all characters as long as they're on the same server. If you buy them or gift them to her on the NA server and then she chooses to play on EU those items won't be available (and vice versa) but otherwise they'll be there for whichever character she creates or logs into.

You can't gift crowns but you can gift most things from the crown store, and that's probably a better option than continuing to play and make purchases on her account, because technically that counts as either sharing an account or trading it and either way it's against the TOS. I don't think ZOS would have a problem with what you've done so far, but it could potentially be an issue if the ownership of the account is called into question later on (say for example if she needs to contact support about a problem with a purchase) and the less activity there's been before she takes it over the better it's likely to be.

All crown store items are account wide on the server they were bought on. You can gift most crown store items but not crowns.