I'm sorry to hear that you still have problems.
1. About the recharging: I have noticed that short recharges seem to confuse the battery indicator bars and give incorrect readings. Try an overnight mains recharge.
(Maybe also see this thread
https://www.mobileread.com/forums/showthread.php?t=21337)
2. If you somehow manage to have books on your Reader which aren't on the connect/ebook library software (--perhaps they got inadvertently deleted) then plug the Reader into the computer, open the connect/ebook library software, view the list of books on your Reader, then drag and drop the book from the reader to the library.
3. You can easily get all the books from your 'My books' folder into the connect/ebook software. In the connect/ebook software, click on 'File' then on 'import folders' and import your entire 'My books' folder.
(If the books are already in the connect/ebook library software then you won't get duplicates, but any unimported books will now appear.)
Leave the original files in 'My Books'. That is where they live. The connect/ebook library software is a big filing system which links to the files stored elsewhere in your computer. If you have been deleting them then no wonder you have had problems.
4. You shouldn't have both the connect software and the ebook library software on the same computer. Ebook library is an update for connect. This may be causing confusion.
Incidentally, it is probably best to call your device a Reader, a Sony Reader or a PRS500. 'Ereader' is proprietary
software, not supported by the PRS500, so confusion is possible.
I'm afraid that I don't use sd cards, so can't really help you on that one. If no-one else replies in the next day or so, then ask again, in a new thread.