Tabatha,
Do you have an option to upgrade at the moment? If so, I'd highly recommend upgrading to v10 to get a huge bucket of feature and performance enhancements.
Kentico 9 Release Notes
Kentico 10 Release Notes
Looking specifically at your questions:
1. Check out the best practices for EMS in v10. Since you're on v8.1 I'd suggest at least what Kentico 10 has for specs.
2. You need to manage this through subscribers and and newsletters.
3. With the EMS license you have the option to use several SMTP servers.
4. Storing sent emails in Kentico is a feature. You can also specify how long those emails are stored within Kentico. Keeping in mind it stores the raw email that is output so that table can get quite large in size if you sent a lot of emails and store them for a long time. So once you set your business practice up, adjust the settings as need to retain your emails.
5. Click throughs are handled like any other email marketing system. Check out the documentation with some screenshots.
6. You can create responsive emails within an external editor and paste the raw HTML and css into a template within Kentico. In v11 (expected out Dec 2017) will have better email template building experience with testing abilities for responsive and such.