If I thaw a steak, will it be safe to eat if I re-freeze it and thaw it again later in the week?

It could be safe to eat if thawed in the fridge.. but the sooner you freeze again the better. Also, expect it to be less juicy.. as the ice crystals puncture the cell walls and the contents of those cells are lost not once but twice this way. Don't refreeze if you thawed it outside of the fridge (if in this danger zone of 40°F–140°F (4°C–60°C)—for more than two hours) as this can culture harmful bacteria that might get you rather sick.