Midfielder Razak, who spent time on loan at Portsmouth earlier in the season, will join Brighton until the end of the season.
"Abdul is the type of midfielder I have wanted to bring into the squad for some time," Brighton boss Gus Poyet said. "He is someone we have been aware of for a while, and we have been patient - but now I am very pleased he is here because he offers something different to what we have.
"He has the type of characteristics of a midfielder I want to bring - the strength, the power to go box to box, the technical ability. He brings plenty of things we didn't have within the squad before he arrived."
Israeli winger Assulin, meanwhile, joins until March 19. He signed for City on a free transfer in December 2010 after leaving Barcelona, and had been close to loan moves to Nottingham Forest and Barnsley earlier in the season.
He has recently recovered from an injury that has kept him out of action since November.