Comment Subscription to resources (Score 1) 90
Kudos on your dedication to be self taught, but the questions you raised are one of the things that a university is great for. To make a meaningful contribution in mathematically-oriented fields (such as computational neuroscience), you need to have the following:
1) Access to latest journals and papers: This should help answer question (1), (2), and (3) - use the tools others are using. If you find an open-source tool, that is great. But often, people in the field will expect you to use a standard framework that has been vetted by lots of other researchers.
2) Access to latest data and tools: Matlab costs quite a bit (esp. with all the toolboxes that you might require). Most universities give you the license for free.
3) Like minded individuals are (for better or worse) almost all at universities and research labs and the main interactions come from conferences. Journals are good for non-interactive peer review, but if you want collaborators, you need to head to conferences. This is also where the university name (and financial backing) can help - "Oh, you work with $BigName? I'd love to collaborate with you!"
You don't have to spend a lot of money either. You can take non-degree enrollment (so you can work at your own pace) while still having a lot of access to the tools, data, and collaborators. In addition, you haven't mentioned your background. So you might find it harder or make trivial mistakes that betray your inexperience or out-of-field characteristics. Most graduate (including Ph.D.) students take a lot of classes on basics (at the start) so that they know the vocabulary and concepts necessary to read and understand the cutting edge research. Without that, you are likely too dependent on the tool. I have known lots of people in industry who swear by Matlab (for example), while not realizing how poor it is compared to more sophisticated optimization tools, especially when you get into large data-sets (which I assume you will be involved with).