The one's I can answer:
1. Are courses created within your LMS opened for search engines indexation?
This is a setting, they can be or they can't be. If you're looking for very good search engine optimization, having a Wordpress portal to display the courses, then link to Moodle using Single Sign-on might be better.
3. Does your LMS allow optimizing images alt tags?
Yes, every image can be alt tagged.
4. Does your LMS integrate with Google Analytics?
6. Does your system allow adding links to course developer website?
Not sure what this means, if you mean a simple link in the course description, then yes, that's possible.
7. Does your LMS allow customizing course URLs?
You can make it have a more meaningful URL with the Local Analytics plugin. I'm not sure if there are other options, it could have to be something that needs to be custom developed.
8. Can courses, created within your LMS, be linked from one main page that is accessible for search engines?
Yes for example Wordpress
11. Is your LMS mobile friendly?