How can I set up new Kindle Fire? - Amazon Kindle 2

Have you set up Free Time app that she can use? I recommend you check this link that give some general help topics. First I'd say take a look at set up Parental Controls, Then how to set up Free Time App. You can block her downloading You Tube and keep her out of other areas she shouldn't be in. You may need to set up a new password so she can't get access to the main menu. Then you unlock it when you hand it over.
https://smile.amazon.com/gp/help/customer/display.html/ref=?ie=UTF8&nodeId=201756690

Yes, Kindle is a name used for all the Amazon tablets and e-readers.

Kindle 2, 4, 5, 7, 8
Kindle DX
Kindle Touch
Kindle paperwhite (1,2,3 generation)
Kindle Voyage
Kindle Oasis
Kindle FIre 7
Kindle Fire HD 6, 7, 8, 8.9, 10
Kindle Fire HDX 7, 8.9

And I probably missed some in here.

Check the Serial Number You can find this sixteen digit code in the box your Kindle came in or when you click on Settings and go to Device Info. Find your specific generation or type based on the first four characters. Kindle 2: B002, B003 Kindle DX: B004, B005, B009 Kindle 4: B00E, B023, 9023 Kindle 5: B012 Kindle Keyboard: B006, B008, B00A Kindle Paperwhite (2012): B024, B01B, B01C, B01D, B01F Kindle Paperwhite (2013): B0D4 or 90D4 Kindle Touch: B00F, B010, B011 Kindle Fire (2011): D01E Kindle Fire (2012): D026 Kindle Fire HD 7(2012): D025 and D059 Kindle Fire HD 7(2013): 00D3 and 00D2 Kindle Fire HD 8.9: B0C9, B0CA, B0CB, and B0CC Kindle Fire HDX 7: D0FB, 00FB, 00FC, 0072, 00FD, 00FE, 0073, 006C, 006D, 006E Kindle Fire HDX 8.9: 0018, 0057, 005E, 00F3, 0019, 0058, 007D, 007E, 007F - See more at: http://glyde.com/glydecast/how-to/which-kindle-do-you-have/#sthash.bAbYPdzQ.dpuf

Press and release the "Power" button to activate your second-generation Kindle Fire or Kindle Fire HD. Swipe down from the top of the screen to display the device options, and then tap "More" to display the Settings menu. Tap "Device" and select "Reset to Factory Defaults." How to Reset Locked Kindle Fire

Amazon.com: Customer Discussions: Kindle won't accept new credit ...

www.amazon.com/forum/kindle?_encoding...

Amazon.com, Inc.Dec 29, 2014 - I have recorded my new credit card details on Amazon Kindle on mycomputer, but my Kindle ... Click on Your Account at the top of this screen, then go down to Settings, then 1-Click ... I changed my credit card info and it still won't acceptit on my kindle ... Go back to your MYCD page and click on devices. How do I re-register my new ...
Mar 11, 2014
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Jan 16, 2012
Kindle Fire won't accept my wi ...
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Amazon.com Help: Register Your Kindle (5th

What you really need to do is add your new Kindle device to your
existing Amazon Kindle account. The good news is if you bought it from Amazon new, Amazon automatically registers it to your existing account. So . . .

Go to the Amazon website using your laptop or desktop computer and log onto your Amazon account.

1)On the upper right of the page you should see *Hello (your name)*
Drop down this menu by hovering your mouse pointer on it.

2) Select *Manage your content and devices*

3) If you're not logged in, enter your Username and password.

4) If you're browser is set to save passwords an log in you won't
need to do step 3

5) Select the *Your Devices* tab

6) All your Kindle devices should be listed there, including the new
Kindle Fire.

7) You can click on your old Kindle and *deregister* it.

8) You can make your new Kindle Fire your *default device* and
you can edit your other Kindle devices such as any Android
Device onto which you have installed the Kindle App.

9) The default device status ensures new books purchased will
automatically download to that device when it's connected to
the internet via Wi-Fi or 3G depending on what your Kindle Fire
is configured with.

10) You can click on the *Settings* tab to manage your credit card and other information.

Not sure this will manage all questions in one answer, but you could start here, where Amazon offers support for the Kindle fire and accounts:
Fire Kindle Echo Support

I am assuming you want to reset the Kindle Fire to its factory settings.
Check the attached video for procedure.
How to Reset Kindle