Could you please advise about some written tutorials, that give detailed explanation of every element of every screen, step by step, about partitioning and installing Mint 19.1?
I'd guess you are not searching very hard... there are literally hundreds of web pages with instructions and videos on how to install Linux. But it may well be that none of them will show your own exact situation (Linux Mint 19.1, to external SSD). Please expand your thinking... installing Linux Mint 19 is basically the same as Mint 18, or Mint 17. Also, installing Linux Mint is very similar to installing Ubuntu, because Mint is based on Ubuntu.
If you want to leave your internal hard drive plugged in while installing Linux, you should look at many of these installation instructions to help gain an understanding of how Linux identifies drives. You need this understanding so you install Linux to the external... so you don't overwrite your internal drive and erase your Windows. But you have already been warned to backup Windows data, in case you don't do this right.
If the fear of damaging Windows is too great, then unplug your Windows hard drive before installing Linux. You will simply boot on the Linux USB flash drive, and tell the installer to "erase disk and use the entire USB external hard drive" to put Linux. It will setup the partitions and put the bootloader on that drive. Or, even if you goof up with this type of install... nothing is harmed, and just start over. If you install correctly, you just reboot when finished and it works. Then plug Windows back in.... but you will likely have to use your BIOS Boot Menu (when the computer is starting) to get Linux, as it will probably only boot Windows normally. Having 2 operating systems means that you must have a way to choose.... using the BIOS Boot Menu is as good as any other method. You have to be quick to interrupt the boot to choose the non-default system.
When you learn what you're doing, this stuff is all very simple... but it has gotten more complicated in recent years due to differences with BIOS and UEFI firmware on motherboards. But the only way to learn it is to get out online and read about it, then do it. Below are a couple of links that I found on a very quick search.... you can do much better than these. I did not watch the hour-long video though.
Special things I'd suggest during the installation:
1. Do not encrypt your hard drive (or home folder). Encryption brings a level of complexity that is not good for beginners.
2. Do not use "LVM" if you see it on one of the install screens. LVM is a partitioning method and is also too complex for beginners.
3. If you unplug Windows hard drive, you can use the "Erase disk and use entire hard drive". But if you leave the Windows hard drive plugged in, you will need to choose "Something else" so that you can put Linux on the correct external drive. The "Something else" screen (actual title of this screen is "Installation type") is also where you must choose the correct drive (external) for the Linux bootloader.