LuaJIT only provides one package, as far as I can see.
Not sure what that means, a "package" is normally a .deb or a .rpm file or so, that a linux distribution uses to deploy software through package management.
If you think that libluajit.so is the only file produced by luajit, that's wrong, you also need header files to compile anything that uses luajit.
Run "ldd myexecutable" to see where it pulls its dependencies from
There is no lib-folder either, everything got smashed into the /src/, which was the same as what happens on Windows.
Assuming you have built luajit from source, yep, that's possible, every project is free to dump its files where-ever it likes in the project. Right next to the source code has a lot of advantages if you work from a shell (no need to constantly switch directories when building and testing changes).
The final product is created when you do some form of "make install", which mostly does a copy of some generated files to the right spot. You can do system-wide installs, which typically requires super user access, or you can do a user install (Linux is a multi-user system, and you don't want to give all users the right to do system-wide installs :p )
An install typically does make a "lib" directory. For luajit, you'll also get an include directory with the header files.
Is shared building advised?
Depends on what you want to do. Traditionally, Unix systems build everything from source. That yields optimal results for each system. Even today "development tools" is right next to "desktop" in a Linux installer, and you get everything you want.
A second option is to hook into the package management system of the distribution. Make a .rpm or a .deb file for a large distribution like Debian. Supplying your own code in the package, and pulling the other libraries that you need from the central distribution.
If you want to distribute only a program, static linking is probably simpler, as that program runes anywhere.
No "dll" hell?
Fortunately, I have no idea what that means :p
Unix is inherently multi-user, and seperate users and processes are kept separate, sharing is not default (it would be a security risk). Libraries use semantic versioning. You can install whatever in your own space, but it won't affect the system as a whole, only you get both the benefits and the worries :)
As a general rule, you don't do things as super-user. Unlike Windows, there is also no actual need to do it anyway. Sane software allows to be installed anywhere, including in a user home directory.