I will give you some suggestions for each point:
1. There are people who installed a Debian distro on the Galileo Board. You can view these posts where this topic is very well developed.
2. You can check this post where there is a discussion about connecting a mini PCIe 3G card to the Galileo Board. It seems they succesfully connect this 3G card.
3. Yes, it is possible. You can visit this website to apply to the Intel® Galileo University Donation Program: http://galileodonation.intel.com\. Also you can check this other website to learn more about this donation program: https://www-ssl.intel.com/content/www/us/en/education/university/galileo-for-universities.html.
Let us know if these suggestions were helpful for you. Have a nice day!