Windows 10: Start button (except left click) and others dont work with right click

Try the following:

The following downloads new files
Open a Powershell window and at the prompt type (or copy and paste)
DISM /Online /Cleanup-Image /RestoreHealth and press <Return>.

Be patient while this proceeds.
Finally, post back the result, after checking your symptoms.

(If this does not work, the next stage will be an in-place upgrade repair install, which keeps almost everything).

Please advise your windows build:
Windows key + R, type 'winver'

Ok, strange. Proceed with an in-place upgrade repair install... but because you have 10586, the disk/iso you use to be 10586. If you have one, that's fine.

Precede it with this in case sthg has happened to your file system:

From an admin command prompt
[Windows key + X, click command prompt (admin)]
chkdsk C: /F
Your PC will need to restart.
Make sure the result is clear or fixed.
Post back the result, which you can get after a restart as follows:
How do I see the results of a CHKDSK that ran on boot? - Ask Leo!

An In-place upgrade repair install will fix many things, but not those where the settings are not changed by the procedure.

For this you need an installation medium with the same base build as you have installed, and x64 if you have a 64 bits OS, else x86 (32 bits).

Repair Install Windows 10 with an In-place Upgrade - Windows 10 Forums
- this includes a link from which you can obtain Windows 10 iso file (" download a Windows 10 ISO"), or create a bootable medium.

I would recommend creating the bootable medium, as this can be used
- for any future in-place upgrade repair install
- to boot from and use its recovery options should Windows become unbootable.
- to clean install Windows

This will refresh Windows, after the manner of a Windows installation.
- all/most associations will be unchanged
- all your programs will be left installed
- you will lose any custom fonts
- you will lose any customised system icons
- you may need to re-establish your Wi-Fi connection
- you will need to redo Windows updates subsequent to the build you have used for the repair install
- Windows.old will be created
- system restore will be turned off- you should turn it on again and I recommend you manually schedule a daily restore point.
- you will need to redo any language downloads including the display language if you changed that)
- inactive title bar colouring (if used) will be reset to default
- if Qttabbar is installed, you need to re-enable it in explorer (Options, check Qttabbar)
This is one of the better features of Win10: as each major build comes out, that's your updated reference build, and as updates are mostly cumulative, there will be few to do.

Recommendation:
Before you perform this major repair procedure, do create a disk image.

Please consider using disk imaging regularly. It's a brilliant way to
- preserve your system (and your sanity)
- back up your data
- restore your system to a previously working state in a relatively short time

Recommended: Macrium Reflect (free/commercial) + boot disk/device + large enough external storage medium.