What guenter said in other words:
A *.7z file is a 7-Zip
archive, like a ZIP archive. It has nothing to do with Windows Installer. You cannot install it, you can only extract it with a capable packer.
Simply extract the *.7z files to a location of your choice (just don't extract them on top of an existing km installation). Before you start k-meleon.exe for the first time, create a new text file in that directory (where k-meleon.exe resides) and rename it to "profile.ini" (not "profile.ini.txt"). Km 1.5a1 (any km since 1.0) will then create and use its own profile located inside the installation directory. This way, you can use multiple km installations with each of them using its own profile. This will avoid profile conflicts.
When you are missing menu items, your probaly in lack of msvcp71.dll and msvcr71.dll. These Microsoft libraries are not included in any of the *.7z packages of km (for legal reasons). They're only included in the km installer (*.exe) packages. Simply copy these files from your existing km 1.1.x installation into the installation directory of km 1.5a1 (next to k-meleon.exe).
This is the first time I have worked with an application that is in ALPHA stage, so please let me know if I am just being impataint.
You only have to know about the things I've mentioned above when you want to use any of km's 7z packages (these are for more experienced users). ALPHA version simply means that the application is in a very early stage of development. The purpose of an alpha version is to be tested by other developers and experienced users to discover bugs. Alpha versions are actually not addressed to end users (because of the many bugs/lacks). Just be prepared that not everything is working...
The only issue I found that new Tabs do not open on double-click - but that might be my system or I have not found the setting yet.
The tab bar is indeed behaving different from the layer bar in this regard. Look into the Tab Bar options in Preferences (section Mouse Control).
Personally, I liked the layer bar's behavior better (where you could close as well as open layers through double/middle-clicks). Well, we'll see... ;)