What can I do to get an admit in a Neuroscience program?
I completed my PhD doing almost all my research in neuroscience, so I can give you a few tips from my personal experience.

Neuroscience is by nature a very cross-disciplinary field. I was coming from a psychology background, and my classmates had backgrounds ranging from biology to computer science to mathematics to pre-med. You will be at a disadvantage given your relative weakness in biology, but not a very significant one. Your math skills from the bachelors in engineering will serve you well as you learn about neural and systems dynamics, and the chemistry you learned will be of immeasurable use in understanding the biochemistry of the nervous system.
Given your background, you should definitely be able to apply directly to a MS or PhD program without having to retake (too much) undergraduate coursework. Do note that you may be able to get into the program with the caveat that you will be required to take some undergraduate courses during your first year; this was a common practice in my program. Given how long it takes to complete your PhD anyway, it should not delay you much, if at all.

Coming from an IT/engineering background, you may be interested in computational neuroscience, a subfield which attempts to understand how the brain works—both at a systems-level (i.e., whole brain) and cell-level (i.e., individual neurons)—using computational models. There are entire departments dedicated to such research; it's a fairly large field.

Your action items listed above are all excellent ideas, and should serve you very well. The only suggestion I would add is to simply google the term &quot;neuroscience research labs&quot; and begin browsing around the web to see what types of research is being performed. As you search, google again using narrower terms, to see how broad each subfield is. Consider writing down some of the schools that house labs that sound interesting to you for future reference.