Question

which laws authorized the president to arrest and deport immigrants who criticized the federal government and limited the free speech of Americas?

Answer 1

There were 4 acts passed in 1798 that are collectively referred to as the Alien and Sedition Acts:
The Alien Friends Act sanctioned confinement and deportation of non-denizens who were deemed hazardous. 
The Alien Enemy Act sanctioned the same for those from a truculent country. 
The Sedition Act criminalized making erroneous verbal expressions that were critical of the regime. 
The Naturalization Act made it harder for an immigrant to become a denizen.