Install Ubuntu as backup OS in an ext. HDD which has 1 more partition

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A few years ago, yes. But now there is UEFI in addition to the classical BIOS boot system. In BIOS, a standard installed system will work well (and is portable, if you avoid proprietary drivers for graphics and wifi) in computers ruing in BIOS mode. But if you install in UEFI mode, a standard installed system will work well (is not portable).

I made some systems, that are portable between UEFI and BIOS mode,

1. Persistent live system, see this link: mkusb/persistent

2. Portable installed system (for cases like yours), see this link: Portable installed system booting from UEFI & BIOS

I suggest that you try both systems and settle with the system you prefer. It is probably easier to start from the compressed image files, that I have uploaded, but there should be instructions enogh for you to create your own custom made system.

The compressed image files will overwrite the target drive, so you must copy all important files from your 2 TB drive to a safe place before using the compressed image files. You need an extra backup in any case because installing an operating system is risky.

Edit: At least until recently, Windows will only read the first partition (logical number one), which is prepared in the persistent live system. Partition #1 is an NTFS partition, that can be used to transfer files between ruing Windows systems and linux systems (including the system on the drive). I think it is more flexible in drives with a GUID partition table (GPT).