Can an old iPad see my iMessages/emails after resetting content and settings? I gave my old iPad to an ex, and before doing so, I deleted all content and reset. I think she may be seeing my iMessages and e-mails. Is this possible?

I used to use the Wi-Fi in her apartment for both new iPad, my iPhone, and old iPad she now has. If I use Find my iPhone to list devices from my iPhone, all 3 devices show up, but the old iPad shows offline. Is there a way of checking what devices have access without asking her obviously?
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.