How to study Ayurveda, yoga, Buddhism, and organic cultivation from Sikkim?

Please note that any foreign student can apply for admission in any recognised university in Sikkim and India will grant Visas to students who procured a seat to study in any recognised university in India including Sikkim. You will get a student Visa.
you can learn Ayurveda, yoga, Buddhism, and organic cultivation courses from any of the recognised universities in Sikkim. But without getting a seat and as a freelancer getting a student Visa is difficult.
So first of all, you take a decision about the courses you wanted to study. Then go to the websites of various institutions in Sikkim and select the course. Then you have to apply as per the procedure mentioned there and then you have to follow the procedure prescribed by the institution. Some universities may conduct entrance tests for admission and some may not.
For example, Sikkim University is a well-known institute in that State recognised by UGC. Its website is www.cus.ac.in. You can get into their site and see what the courses they are offering and you can select the one you wanted and apply when the notification for admissions is released. Please note that you can't do two-degree courses simultaneously. But you can do one regular degree and another diploma course on a part-time basis or distance mode can be done simultaneously.
There are about 25 universities in Sikkim having UGC recognition. Get the full information about those universities and the courses they are offering. Select the course, and apply. Once you get a seat, you will be granted Student Visa if you have a valid passport given by your native country.

As far as admission is concerned regarding the foreign students, if they choose some recognised universities for continuation of their studies, they will be provided students visa for their ongoing studies and the same point applies to Sikkim University.
You need to know the details of the courses offered by this university by going through the website for the courses being taken up the university or alternatively you can visit the university and can know the details of the course structure of the given university. You need to ensure its recognition status even by going through the UGC list.
The courses being mentioned by you for taking up such courses for the regular session, only one course is permitted at a time. Suppose you want to persuade Ayurveda Course, you need to appear for the medical test and on clearance of the same, you can go ahead for this course leading to completion of BAMS course which allows you to indulge in Ayurvedic Medicine Practices allowing to enjoy a registration number. If you would like to have a post graduation degree, you need continue your studies further for three years so as to get a degree of M.D. in Ayurveda.
If you want to continue for Ayurveda and Yoga course, look for its provision in any university currently 25 in number enjoying UGC status.
For Buddhist Studies and Organic Cultivation, you may refer to university site to know their details of the course structure. In this context, please note that two degree courses cannot be taken up simultaneously and at least either of the course should be a diploma course to match the eligibility criteria of the university.