The question is about installing GRUB on USB drive. Let's start with the questions first:

1. The command sudo grub-install /dev/sdb (where sdb is my USB drive) should work when booted from the hard drive with USB drive connected. However, since GRUB puts its config files in /boot/grub, where those will go depends on what kind of Ubuntu installation you have in the USB drive.

   
   
   
   
   
   • If it is a live USB, the /boot/grub folder includes a loopback.cfg
     and installing the rest of grub there may have unintended effects.
   
   

   • If you have a full installation of Ubuntu in a 8GB or larger USB drive, See more at
     How do I install Ubuntu to a USB key? (without using Startup Disk Creator),
     then GRUB should be installed at the time of Ubuntu installation. If
     for some reason GRUB is not installed, you can mount the USB boot
     partion (assuming sdb1) and specify where the rest of grub goes by

     
     
     

     sudo mount /dev/sdb1 /mnt
     
     sudo grub-install –boot-directory=/mnt/boot /dev/sdb
     
     

   
   



2. Yes, you can get a GRUB menu from USB drive provided you have a full Ubuntu installation in that USB drive.




3. No, update grub should not delete information from the internal drive. You can control which GRUB will be updated by using sudo chroot /mnt after mounting sdb1 to mnt.

Hope this helps.