[stumped]

for chrome etc you get it from the installed playstore so you get the safe, official versions
if you installed the relevant apps for google accounts, services, store, in correct order you should be able to use the play store, just like on a proper android tablet. ( but it takes a while for play store etc to fully start up- i think it has to complete some one-off background scans and tasks before it completely works )

your books open ok in moon reader , and in calibre viewer, so there is no actual DRM in them. its a bug in the kindle reader app. You could try the same books in kindle for PC to confirm that its only the tablet app that has the issue

I'd be inclined to do a full factory reset and start over, to see if all the misc problems go away, if not get a cheap new one in black Friday sale, or something different , if you had it with fire tablets - then sell yours as for parts/ not working ( full disclosure on ebay) someone will take if off your hands. Sell it after the BF sale ends for a better price.

several sites have the detailed steps & links for adding google services. or you can have a link to what I use if you Pm me with an email address to share to