Actually, you are already in an online university and technically you would be a transfer student, so you may not need to take the SAT (at least for Extension). You will need proof of English proficiency, usually by taking the TOEFL test, but Extension may accept your English Prep class that you took online.
The Extension web site isn’t clear on everything, so you may have to send an email and explain your situation (leave out the mental health parts, though). Ask for advice on how to proceed and what you need to do in order to apply. The Extension has three application deadlines a year.
While Harvard Extension is an excellent program for the older/non-traditional student (and they do offer financial aid), I don’t know how much support you’re going to get in terms of paying for the application fee, applying and paying for a visa, getting to the visa interview, paying for flight to Boston, down payments on housing, etc. etc. That is all beyond my knowledge base. Harvard is likely to be a good guide, but first you need to get accepted. There lies the real challenge.