Let me know if you need elaboration anywhere :)
For you, you want all the countries to be hidden, and only the countries that are randomly selected to show up, right? So to do this, we need every path (in this case country) to have a class which is the same, so that we can use CSS to hide them all at the start. It would normally be easier to just select everything in Inkscape and set to opacity 0, however JetPunk's minifier for SVGs automatically removes any paths with opacity 0, so that won't help us.
My suggestion of using the "country" class was if you were using the JetPunk map.
To your second point, unfortunately no not easily. You can do it with some PHP and a script, but I sense you're not a programmer so manually changing them will be easiest. :)
Feel free to keep firing away any more questions :)
Then, you need to organise your groups in Step 2. The editor will show you the boundaries of each group, and you just need to put in groups of countries. It might be easiest to do this in a spreadsheet to maximise your number of groups (to give a large enough pool). Essentially you need to hard-code the groups themselves into Step 2, there's no way to tell the randomizer to pick "groups of countries" other than to group them manually and use "random group".