A couple of things were not mentioned in the accepted answer:
documentation associated with the software
BSD-2-Clause Plus Patent aka "BSD+Patent"
Another difference between the BSD licenses and the MIT license is how they deal with the meaning of "software".
MIT applies to the documentation associated with the software, ...
In the meantime, the project has been relicensed under MIT and patent grants were removed.
The original PATENTS file is here:
Curiously, the MIT licence does not provide patent protection for contributors. So this seems to be a step ...
Yes, that is allowed.
The license explicitly gives permission to distribute the software with modifications. The only conditions to that are that you retain the copyright notice and license text.
For your changes, you can put in your own copyright notice.
Ask any contributors to make clear their contributions are under the same license, and that they are legal owners of the contributions (not swizzled from somewhere else), and that they give up any patent rights and so on. Check for some large project using your license, exactly how they do it.
It is just a tool you are using. Ship it just the way you got it (binaries, documentation) and mention somewhere that you are using that tool, where it is found in whatever you ship, what changes you made --if any--, where to get the original, upstream version). The unrar license mostly says you are not allowed to base a compression program compatible with ...
You should not modify the notices in any way and reproduce them verbatim. If the copyright notice says “all rights reserved” leave it be. This is the “default license” anyway. The license text then goes on to grant specific rights, so this is not a restriction on your rights.
Under older copyright regimes (the 1910 Buenos Aires convention), a notice like “...