http://www.securitytube.net/ https://www.pentesteracademy.com/ ... both run by same company

Can a F1,J1 or H1B visa holder register a company outside USA (home country) ? assuming it doesn't void any contract between said person and his/her employer or sponsor.

From an immigration standpoint, there's no issue but I suspect that there are corporate and tax factors that should be considered as well.