ok, I've been in touch with Apple chatting and talking with them on the phone for 2 hours.
The first suggestion was to delete the iBooks folder. We didn't get to do it because they phoned me and I had a different representative from Apple who wanted to check all sorts of other things. I'm not going into any details because this is a really long story.
Today I went through the problem again on my own. To make it short I found out the following:
Using my regular account downloading already purchased books results in a number of messages being logged to the console:
10/10/15 12:48:42,219 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,225 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,230 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,236 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,242 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,246 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,247 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,253 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,258 | storeaccountd[447] | XPC error for connection com.apple.backupd.sandbox.xpc: Connection invalid |
10/10/15 12:48:42,268 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,272 | com.apple.SecurityServer[89] | Session 100047 created |
10/10/15 12:48:42,299 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,331 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,361 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,369 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,375 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:42,381 | sandboxd[142] | ([447]) storeaccountd(447) deny mach-lookup com.apple.backupd.sandbox.xpc |
10/10/15 12:48:43,907 | storedownloadd[601] | SSDownloadAsset caching-server-locator-timeout 10 |
10/10/15 12:48:43,938 | storedownloadd[601] | AssetDownloadOperation no modified URL for http://a203.phobos.apple.com/eu/r30/Publication1/v4/c4/47/db/SOME_PRIVATE_DATA_R EMOVED |
10/10/15 12:49:02,000 | kernel[0] | Sandbox: iBooks(1535) deny(1) mach-lookup com.apple.dock.appstore |
10/10/15 12:49:04,659 | com.apple.SecurityServer[89] | Killing auth hosts |
10/10/15 12:49:04,659 | com.apple.SecurityServer[89] | Session 100046 destroyed |
Obviously, El Capitan broke something. Similar problems are shown on http://apple.stackexchange.com/questions/208292/cant-login-in-mac-app-store-or-i cloud-login-loading-forever .
Now, the "weird" thing is, that I can download the books using a different user without problems. Currently it is no option to move everything to a new user since a lot of settings, emails, ... would either be lost or would need to be recreated.
Finding this out took me only 10 minutes. I kind of wonder why Apple didn't ask me for the logs. Instead they suggested that my internet connection is too slow. Well of course it is slow connecting to the Apple servers when there is high load on them and sandboxd tries to download stuff and keeps getting errors.
Wonder when Apple is going to fix this problem.