iTunes wont backup 5 iPad apps [authorize issue]

Ive used Macs since the 80's, have multiple iPads, Macs, iCloud accts, Apple IDs etc... no novice, big user.

Problem:

I recently bought a 2nd hand iPad from a retail tech. shop here in NL.

Its been formatted, cleared, factory set, out the box new-like.

I synced the new iPad to my iMac iTunes no problem.

I installed an app "Paper" to the iPad and it works. Great.

After a few wks, Paper is beginning to crash repeatedly.

Solution: All info needs backed-up [iMac] & app reinstalled.

iTunes wont allow the back-up. I get repeatedly "Cant Authorise this computer" error. Not logical / true.

Cant delete & reinstall until I backup the info.

Suspects:

- Restart both machines, didnt work.

- iMac iTunes > File > Authorise = it already is [message].

Ive got two main Apple ID accts, I bounce between:

- Sign out of one into the other, authorise didnt work, it already is.

Neither will backup.

Checked Apple community =

- Remove iMac SC Info file, Did. Didnt work.

iMac sav didnt work = Try iCloud backup:

- iCloud wont allow anymore accounts on the iPad. There are none connected. What? Wheres this coming from?

Q: Could the iPad have NOT been totally wiped clean from the store I bought it from?

STUMPED. Need solution without losing all info on 5 apps that wont backup...

- Evernote, Paper, etc...

Whats next?

I have a holiday next week and the ipad isnt available all next week.

Im really close to calling apple n going into the store for Mac experts.

Yet it wasnt bought through them so they wont be so helpful from the start.

That experience will take hours of my life. This already has.

Please, any help is very apprecaited thx guys! U ROCK!

HELP. THX 😀

Brian

Frustrated in Amsterdam