Can I develop using my favorite IDE instead of Eclipse?
Unfortunately, the easy answer is "no". Until somebody ports Bndtools to your favorite IDE, you either have to use Eclipse, or a combination of your IDE and manual builds using Ant (though not recommended). If you insist, please do make sure you manually generate the proper metadata for Eclipse.
How do I build this thing in Eclipse?
Normally, you don't. Seriously. As soon as you hit save after changing a line of code, BndTools will automatically build your bundle for you. In fact, if your server if already running, Bndtools will even redeploy all changed bundles to it automatically.
I see lots of red crosses on my projects and complaints about missing test libraries!
You probably forgot to install the TestNG plugin. If this plugin is installed, it will automatically cause your projects to get the required dependency to the TestNG library. Without this plugin, Eclipse won't have the required library and fails to compile the code correctly.