In a dual boot ubuntu 14.04 / windows 8 (upgraded to Windows 10) laptop, there's no entry in the grub menu list for starting the windows 8 recovery procedure (installation files are in a partition). The only windows-related entry is "windows boot manager" and it makes windows 8 normally start. In the grub.cfg file in fact there's no menuentry starting at /dev/sda1 which is the partition labeled as "Recovery", nor a menuentry starting at /dev/sda9 which is another ntfs partition labeled as "Push Button Reset". The "system setup" menuentry just starts the bios by the command fwsetup. Is there any way to make grub find the recovery partition?
Booting to advanced options and safe mode is still possible, when you have GRUB in the boot chain you need to press the keys right after GRUB loads the Windows loader. If you have a UEFI system you should try to change the order of the boot options or issue to boot Windows at the next boot and try from within Windows to get to the advanced options menu.
I think I got a virus on Windows, and I want to use the installation partition to reinstall windows. I don't mean the procedure which just removes data and settings, but the procedure that formats and reinstalls windows.
As far as I know the installation data for the "refresh my PC feature" is on the main filesystem, which therefore cannot be "formatted", because there is usually not enough space on the other filesystems to store the data and there are no mechanisms like a PXE environment involved (similar to how Macs perform a reinstall). You're not doing a complete reinstall this way as far as I am aware and you have no prove that the content hasn't been modified by the virus you expect to have infected your system. After all the data was on the same filesystem and you shouldn't expect a virus to be as dumb as not to do a simple mountvol and get access to the other filesystems.
Getting the installation media from Microsoft and verifying the checksums is what you should do.