My keyboard also stopped working when I downloaded Aptoide.
The fix is a combination of things.
1) Your touch screen should still work. Look for Settings > Keyboard & Language > Current Keyboard. There is going to be Swype. I believe Aptoide deletes the original keyboard.
1) Go to Appstore > Categories > Utilities > Subcategories > Keyboards
There will be top sections:
A "Top Free in Keyboards" or
B "Top Paid in Keyboards"
I choose the free "TalkType Voice Keyboard" as I wasn't going to buy "Swype" which made me do all this or the Aptoide App.
This worked for my Fire Tablet 10HD
Using Fire OS 126.96.36.199 on Jan 2018.
Oh I forgot go back to step 1 and change the Current Keyboard.
This should get you a keyboard back. The one I choose TalkType is good. It's a little fancy. But I can just use the regular keyboard - no need to use voice. Plus I can download other keyboards can switch to a new one. Also downloaded: FancyKey Keyboard and American Keyboard Pro. You need to open the apps to set them up.
Go to Settings > Keyboard & Language
Slide to right and it will to up to let you choose it.