Ok, I'll work my way down the list of questions.
 
yes, part is encrypted, but nothing "extra" needs to be installed or loaded on the server to make it work.  Mostly the administration functions are enc'd.  We don't really authorize anyone to modify the actual code of the script, unless explicit permissions are given after an explaination of why the code needs to be modified.  Mainly because people modify it, say its broke, and then we spend a while troubleshooting a problem only to find that indeed they did modify the script despite the fact that they said they didn't.
 
No, script is pretty secure, we've tried everything we know, and had some folks "in the biz" give it a go, so far we haven't found any holes.  But a lot of that has to do with your server configuration as well.  Just because the script is secure, doesn't mean your hosting account is, so be weary of that when selecting a hosting provider.
 
Most everything is customizable.  Everything your members see is template driven.  You modify the templates to your liking.
 
There's not many non-password protected areas to the script, so google would be able to crawl the index page, password request page, contact form, and the resend validation link page.  No bot is going to actually login to the script and get member information.  All that is password protected and I don't know that I've ever seen googlebot doing brute force password cracking.
 
Well there's not anything you can do with the script without some type of address on the internet.  My recommendation would be to come up with your domain name, purchase it, and then purchase the script.  No, we can't make the license apply to any domain, that would pretty much defeat the purpose of having a license key at all.
 
If you have any more questions, don't hesitate to ask.

Yes, its no problem to remove the logo later on, just let us know and we'll give you full instructions.