The best option is to e-mail the school you are going, and ask for a copy of degree audit checklist or degree requirement checklist, which usually list the required and elective courses you'll need to complete for a certain degree.
You may also ask for a course schedule and an academic calendar of the recent academic year and get an idea on which semester/trimester and time slots were those courses made available. And in the calendar you can get a gist of when is the start and end of the semesters/trimesters, last date for adding/dropping courses, etc.
Lastly, some schools may include the degree requirement information in their student handbook. It wouldn't hurt to ask or search for a PDF copy of the handbook as well. You should also find details on cross registration to other institutes. Also be careful that universities tend to have a handbook for the whole study body, and then the smaller departments within them may also have their own smaller handbooks. Make sure to get all the copies that are related to your degree.
These terms should give you a good start. But do bear in mind that by the time you start to study, some of the information may be updated in the new academic year. So, you may plan, but be ready to be flexible.
As for if you can work with one or more professor on research. The answer would depend on many things: some students got assistantship to help the professors, some work as if the professors hire them, some work for academic credit (as a directed study.) There are too many variations that I doubt you will find a single document telling you everything. This question is probably best asked on the orientation day once you arrived there.
As for digging into their site, try to use some suffix in Google to enhance your results. For instance, try to search for
degree requirement checklist site:MyInstitute.edu to confine the results from the domain of
www.MyInstitue.edu. You can also modify it into
degree requirement checklist site:MyInstitute.edu filetype:pdf to search for only PDF documents.
Good luck with the planning.