A few things you can try:
Open Settings->General->Reset->Reset Keyboard Dictionary
You could also Reset All Settings but you will have to set your wallpaper again, log back into any wifi network(s) etc but won't lose any data.
Settings->Safari->Clear History & Website Data
Turn off Safari in iCloud Then turn back on.
SIgn out of iCloud on your device then sign back in.
To free up some space:
Settings->General->Storage & iCloud Usage->Storage->Manage Storage...
Any apps like Facebook, Spotify & Twitter build up a cache over time & the only way to remove it is by deleting & reinstalling the apps. A bit of a pain but it can make a huge difference,
As far as your email, you might want to try removing the email account from your iPad then re-adding it.
I am running iOS 9.02 on my iPad 2. I have also sometimes experience lag when typing but for me, it is almost always related to iCloud. Since many apps are now tied to iCloud & sync between devices almost instantly, this can cause a lag in typing when there is an issue with iCloud. At least that's the case for me,