I run this on my Ubuntu Linux server. It's awesome and I've always gotten great support.
- Import subscribers with CSV
Yep, you can do this. I make fairly extensive use of this feature.
- Export subscribers to CSV
Yes.
Not sure what you mean - but if you mean that it can send email to multiple people with one click, yes. I currently have a list of ~15k subscribers, and my t1.micro (really small) server doesn't choke on it.
- Multiple newsletter management
You can have multiple brands, multiple lists within a brand, multiple newsletters for each list (and multiple lists each newsletter is sent to), and even have scheduled emails that are sent to a subscriber after they've been subscribed for x days.
- Click tracking per subscriber
- Analytics / Graphs
For a list:

And for a single email, you get stats/pie charts on how many people opened it, what country they're in, what they did after they opened the email, what links they clicked, etc. I can't show a screenshot of this for obvious reasons, but it's just as beautiful as the rest of the app.
No, these aren't included in Sendy. I personally like to have my emails have a 'personal look' - no fancy colors, borders, etc. But there are plenty available on the Internet.
It's not open source, but it's very easy to modify with even a very slight grasp of PHP. I've done it. They don't obfuscate the code or do anything evil like that:
Are Sendy's files obfuscated?
Sendy's files are not obfuscated except for the installation and functions file. You can edit the source code for your own personal use without needing these two files.
It's currently $60, and it's well worth it. It includes a fancy API that I make extensive use of from my apps, and it simply looks good. It is designed to run off Amazon SES, with a grand price of $0.10 per thousand emails. It can also run off straight SMTP from your server, though. I prefer SES myself.
You can try out a live demo here.