  In this paper, which completes our earlier short publication [Phys. Rev.
Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP)
performing a biased random walk in an adsorbed monolayer, composed of mobile
hard-core particles undergoing continuous exchanges with a vapor phase. In
terms of an approximate approach, based on the decoupling of the third-order
correlation functions, we obtain the density profiles of the monolayer
particles around the TP and derive the force-velocity relation, determining the
TP terminal velocity, V_{tr}, as the function of the magnitude of external bias
and other system's parameters. Asymptotic forms of the monolayer particles
density profiles at large separations from the TP, and behavior of V_{tr} in
the limit of small external bias are found explicitly.
