Чем Kali Linux отличается от других дистрибутивов Linux тем, что он используется исключительно для взлома и тестирования на проникновение?

I have been asked to first start using Kali Linux and get used to the bash before doing anything in hacking.

No. Just no. "Getting used to the Bash" means you're lacking somewhat fundamental skills and knowledge in Linux. Kali Linux is a fairly focused distro designed for penetration testing. It does have a few unique packages, but it's also set up in somewhat of a strange way.

Using Kali does not make you a hacker. Too many people think so and are completely out of their depth, being unable to do basic tasks in some cases. If you wish to learn the fundamentals the right way, forget about Kali at first. Kali's an Ubuntu fork, and a modern version of Ubuntu has better hardware support. You might also be able to find repositories with the same tools Kali does. That's for later though. Work through something like Linux the hard way or LFS101. Understand the basics. Learn Linux before you get yourself delusions of grandeur. You make yourself a hacker, not the distro.

Kali is a somewhat overrated distro that's specialised, attracts skiddies and doesn't have anything special to offer to the newbie Linux user. You'll find that with a certain degree of hacking skill, you'd probably end up customising your own environment anyway. Kali's really designed for the middle ground where one has basic-good skills but needs a standard, fairly substantial set of tools available. It is certainly a terrible distro for someone who isn't used to Bash or the Linux environment.

Actually, you CAN do everything also on Ubuntu and others. Kali linux is just a pre-configured set of kernel-mods, settings, and applications in a way you would actually use it for penetration testing. If you want to setup everything the same way in Ubuntu, it would require a lot of effort and time, including building your own kernel, compiling specific packages, and also know what software you might want to have.

Usefulness depends very much on what you are planning on doing. I mostly use it to troubleshoot network issues, because it has everything enabled in a way that makes this straightforward. Especially if you're using a Live-CD/-USB, you would not be able to compile a specialized kernel or easily insert kernel-modules (i.e. device drivers).

First off, what is a Linux distribution? This is what Wikipedia says:

A Linux distribution (often called a distro for short) is an operating system made as a software collection based on the Linux kernel and, often, on a package management system.

To put it bluntly, a distro is a Linux kernel plus some software. That's it. The software can be whatever the distro creator wants to distribute with that kernel. For example, some distros come with OpenOffice, some come with KOffice, while some come with LibreOffice.

Generally speaking, you can use any Linux compatible software on any Linux distribution (and even non Linux OSs like BSD). Kali is Debian based, as is Ubuntu. So you can easily install .deb packages on either. However, you are not limited to .deb, just about any Linux software should work. There are packages that will install .rpm packages on Debian based systems.

This means, if you find Ubuntu, Mint, Red Hat, CentOS, Suse, (even BSD) etc a better environment to work in, you can install any software packages you find missing that were in Kali Linux.

As for your second question, that is purely opinion based. Again, generally speaking, you can put any Linux software on any distro, so one could argue that they are all equally useful. Some distros are packaged with less overhead, so they run faster than a more "bloated" distro. Some distros are designed to be a general user's desktop. Some distros package only open source software, while others include closed source. You just have to find, or create, the mix you find best meets your needs.

Kali Linux имеет много встроенных инструментов и поставляется с ним. Вы можете использовать обычный дистрибутив Linux, но вам придется установить и настроить все эти инструменты самостоятельно.

Kali Linux is a distribution designed for penetration testing in that it ships with a whole bunch of different tools for hacking and security testing. Most of the same tools are available on other distributions; it's just that Kali comes with these tools out of the box and ready to go, and does not include non-essential apps like GIMP or LibreOffice that mainstream Linux distributions provide.

If you're not even familiar with the Bash shell, though, then you probably need to do some studying and learn about the fundamentals of Linux first. The tools assume that you have the requisite knowledge to use them, and this means familiarity with the way Linux works and how to use the shell. Kali is designed for the security professional who knows what he/she is doing, and is not really aimed at beginning Linux users or everyday use as a normal Linux distribution.