Colleges in Arunachal Pradesh - Other

Yes, you can register yourself as a practitioner.
Please refer to the link for details: http://ayush.gov.in/acts-rules-and-notifications/guidelines-registration-naturopathy-practitioners-and-accreditation-institutions

As per thier website, Himalayan University is recognized by the UGC - University Grants Commission under Section - 2(f) of the UGC Act, 1956 and hence empowered to impart higher education at all different levels of Under-Graduate and Post-Graduate. Himalayan University is included in the list of approved universities in India listed by UGC Approved Universities. Therefore, degrees awarded by University is valid for Government and Private sector jobs.

Himalayan University is UGC accredited. However, it is relatively a new university and will take some time to establish itself. If you want to pursue a course through distance, you should be okay.

HNB University is a central government university. In my point of view, you can opt for it.

Yes, you can get admission in good colleges by giving GMAT, CAT, XAT, SNAP and colleges oriented exams.