I backed up my data to an external hard drive. Do I need to disconnect the drive before installing Ubuntu?
It is not necessary, but I would suggest to unplug it for safety. This way, you are sure to not format it by mistake.
No, it is not necessary to unplug the external drive, when you intend to install Ubuntu into the internal drive.
But it is a good idea, particularly when you have your backup on that drive. When all partitions are properly unmounted and the drive is unplugged, there is no risk that you overwrite your backup.
The opposite case: It makes things much easier, if you unplug the internal drive, when you intend to install Ubuntu into the external drive.
no, just do not install ubuntu on the external drive
You should not have to disconnect your external HDD when installing Ubuntu. The installer will give you the option of which drive you wish to partition and setup for the OS during the installation and as long as you don't select to install to the external HDD then it will remain untouched by the installer.
I dont see any reasons to take it out or keep it...
If you are worried about it, and do not need it during the installation, might as well take it off! It should not interfere with the installation however... its just another disk....
You can leave it plugged in. Just be aware that you may wind up with extra entries in you GRUB menu if the external drive has any bootable partitions. If that's not what you want you can always use:
After the fact.