The database repair is now built into the MailClient.exe file. If it detects an issue with the database, it will repair it automatically. But if you think you need to repair the database, you can run this command with eM Client closed: "C:\Program Files (x86)\eM Client\MailClient.exe" /dbrepair
To backup eM Client, use the built-in function which you will find by going to Menu > Backup. This does more than just copy files to a zip file. It also checks your database and writes wal data back to the original dat files. You cannot do that manually, so just use the backup function.
You cannot replace single files from one backup to another. They are not individually useful as they are part of a group of files that make up the database. You will just end up with a useless zip file that probably cannot be restored.