Would a website such as solarmovie where movies, tvshows are not hosted at but links are shared or videos are embeded is it illegal and would be shut down?
No, it's won't be shut down. Under Section 512(f) of the Copyright Act, any person who knowingly materially misrepresents that material or activity was removed or disabled by mistake or misidentification may be subject to liability. So it is legal by Digital Millenium Copyright Act.