You have a indeed some problems and I hope we can solve a few.
Problem number 1 and 2 can probably solved by a hard reset.
Problem number 3 happens more it could be related to number 1 or 2 but basically 97% should be enough to get most apps back.
But have a look at this article
Error with your Windows Phone OS backups? Here is how to get them back on track | Windows Central
But be aware that this back up does not back up files like pictures, music documents etc. It "only backs up apps+settings and if you enable it text messages.
But also be aware that if you do a hard rest and restore the back up that apps which are pulled from the store will not be available anymore. (During the apps+settings backup the app is not back upped put the link to the store)
Problem number 4 may be due to a bad USB port in your phone because your already tried different USB cables and PC's
But have a look at this post.
http://forums.windowscentral.com/win...ows-8-1-a.html
Is you still are not able to connect your phone to your PC you could back up your files to Onedrive or use an app like Easy transfer
Easy Transfer: Transfer files from Windows Phone over Wi-Fi
If you need more assistance please register and reply on this post.
Good Luck