I think the lag is the framrate (fps).
You have to look under Options and turn down the settings e.g. dynamic sky doom off, background landscape off, LODs off, multi texturing off, (mutli threading on? ). Test what is perfect for you.
You dont get any damage because your driving skill level is rookie?, go to the player options and set you skill level higher. (set it to pro
) (the ai skill level is in the options -> Ai opponents menu)