IPhone – I sold the old iPhone and it says “offline” will texts messages still show up in it

If your phone gets close to any WiFi network it has been connected to before it will reconnect and receive whatever is pending (iMessages, Mails etc.). Depending on your Notification Center settings and/or the strength of your password (if any) the person holding the phone will then also be able to read them.

But

• are you sure the phone is gone and not just laying somewhere you haven't been looking at?
• you still can use Find My iPhone to erase everything on the phone (which will be executed if the phone goes online again)

No, unless she is using your Apple-ID this will not be possible.
As your old iPad appears offline, this probably is not the case. You can delete your old iPad from the Find my iPhone app in order to tidy up the list, this won't disable any Apple-ID on her iPad though, should that still be on there. If you reset the device though and didn't set up the iPad with YOUR Appe-ID then you're good to go.
Also: notice that when a new device starts using your Apple ID, Apple will send you an email notifying you about that. So you can also check that even for now and in future.