Windows still use DLLs and Mac programs seem to not use DLL at all. Are they benefits or disadvantages of using either technique?
Both use shared libraries, they just use a different name.
If a program installation includes all the DLL it requires so that it will work 100% well, will it be the same as statically linking all the libraries?
Somewhat. When you statically link libraries to a program, you will get a single, very big file, with DLLs, you will have many files.
The statically linked file won't need the "resolve shared libraries" step (which happens while the program loads). A long time ago, loading a static program meant that the whole program was first loaded into RAM and then, the "resolve shared libraries" step happened. Today, only the parts of the program, which are actually executed, are loaded on demand. So with a static program, you don't need to resolve the DLLs. With DLLs, you don't need to load them all at once. So performance wise, they should be on par.
Which leaves the "DLL Hell". Many programs on Windows bring all DLLs they need and they write them into the Windows directory. The net effect is that the last installed programs works and everything else might be broken. But there is a simple workaround: Install the DLLs into the same directory as the EXE. Windows will search the current directory first and then the various Windows paths. This way, you'll waste a bit of disk space but your program will work and, more importantly, you won't break anything else.
One might argue that you shouldn't install DLLs which already exist (with the same version) in the Windows directory but then, you're again vulnerable to some bad app which overwrites the version you need with something that breaks your neck. The drawback is that you must distribute security fixes for your app yourself; you can't rely on Windows Update or similar things to secure your code. This is a tight spot; crackers are making lots of money from security issues and people will not like you when someone steals their banking data because you didn't issue security fixes soon enough.
If you plan to support your application very tightly for many, say, 20 years, installing all DLLs in the program directory is for you. If not, then write code which checks that suitable versions of all DLLs are installed and tell the user about it, so they know why your app suddenly starts to crash.