It's a Dahon folder! There's more joints and rickety bits on that bike to creak, rattle and groan than a catapiller! While you could lightly grease all the sliding fits the bike and you would soon be a mess if you fold and collapse it on a regular basis. Made some sort of dry film lube may prove better for this bike.
As for the freewheel it is supposed to click and must click. When it clicks it says that the ratchet pawls are freely moving and reacting to the teeth going by when you're coasting. Grease will gum the works and not allow the pawls to snap down into each tooth the way they are supposed to. At most dribble some oil into the freewheel through the crack between the part that moves and core that doesn't. But don't dribble it down along the axle opening. Leave the wheel on it's side for a while and keep turning it now and then to distribute the oil around inside to the bearing balls and ratchet teeth and pawls. Then turn it freewheel down over some old newspaper and let the excess drain out for a few hours.