grub-install - use to install GRUB boot loader on your hard disk. There is no relationship exists between GRUB and kernel upgrade. If you run grub-install it will just reinstall GRUB.
In olden days you need to run lilo command after kernel upgrade. First you will edit /etc/lilo.conf with something as follows:
Code:
image=/boot/vmlinuz
label=linux
initrd=/boot/initrd-version.img
read-only
root=/dev/hda2
Once you are sure that /etc/lilo.conf is properly configured for new kernel, run to load new changes and kernel:
However grub can read grub.conf file on fly no need to write MBR again.
This is one big difference between GRUB and LILO: With LILO, every time you rebuild your kernel, you will need to reinstall the boot loader (run sbin/lilo). So, there can be less of a maintenance issue with GRUB. Also you'll need to execute lilo again after any changes are made in /etc/lilo.conf.
Rests of your commands are correct