The two things could be related. . . a lot of books -- like over half the memory used -- can mean response can be a bit sluggish. AND if there are even a very few books that aren't indexing properly, that can eat up battery life.
Of course, on the Fire, other things can impact battery life as well. . .if you spend a lot of time connected and on the web, for example.
You can remove any book from the device by touching and holding the icon and selecting the appropriate option that pops up. It will not be deleted permanently from your Amazon account -- you can only do that via the Amazon website and Manage Your Kindle. But it will no longer show when you select "device" in the books tab. Similarly, you can remove the books from the carousel.
Depending on your preferences, it might be as easy to do a factory reset and then start reloading things. You can do that by pulling down the menu and selecting 'device'. From there you have a number of options, one of which is to reset to factory defaults. You can also check your storage and see what, really, is filling up the memory.
To check battery usage, use one of the various free battery monitor apps, to see what's using the battery even when you think you've shut it down. Here's a good one:
And there's a Free version of it as well if you prefer
