According to Star Trek canon, Pavel Chekov was born in 2245. This movie takes place 10 years after the USS Voyager returned to Earth from the Delta Quadrant (Voyager returned in 2378 according to Star Trek canon, so this would make it 2388), so this would place Chekov's age at approximately 143 years old.
The quote that Lexxa Singh recites is from the poem Invictus by William Ernest Henley
Captain Alvarez is the captain of the USS Archer, which is named after commander Jonathan Archer who was captain of the first interstellar ship Enterprise.
According to Star Trek Canon (as well as "Star Trek: Voyager (1995)" and "Star Trek VI : Terre inconnue (1991)"), Tuvok was born in the year 2264, which would make him 124 years old at the time setting of this film (2388).
"Star Trek: Renegades" is a series of fan films which is a spin-off of "Star Trek" (1966) (TV Series) and it takes place after "Star Trek: Voyager" (1995) (TV Series). The series follows the adventures of a crew of renegades by Lexxa Singh (Adrienne Wilkinson) whom is the direct descendant of Khan Noonien-Singh.