How to restore Windows Store?

The Store tile in Start is today blacked out, as are several important apps such as Mail, News and others. None of them launch and with Store unavailable I cannot try re-installing them. How do I restore the Store? I have some Restore Points which I can try eventually, if there is no other way to restore the Store.

In my experience once the store and those native apps go wrong there is very little that can be done to salvage them. The only 2 options open to you are either a repair install or as you mention system restore. In fact the fact you have restore points set is a great thing. As long as you can remember which one points to a time when all those apps worked. You won't lose anything by doing it. It's saved me before when I totally hosed up the native apps running the powershell 'fix'.

I did restore Store yesterday, after have delete it and also all App by my mistake.
The solution was to re-install all Apps for All Accounts using PowerShell . Have a look here: Apps - Reinstall and Re-register in Windows 8 and 10 - Windows 10 Forums

You can try the following to repair the store. Open a powershell prompt and type the following.

$stores = Get-ChildItem -Path 'C:\Program Files\WindowsApps\' -Filter "*Store*"
foreach ($store in $stores) { Add-AppxPackage - Path "$($store.FullName)\AppxManifest.xml" -Register -DisableDevelopmentMode"}