If you can get the lockring off, removing the pawls and springs usually gives you two 'flats' to clamp in a vice. Or even leave the springs/pawls there if they are sufficiently 'recessed' to avoid damage. May be ultimately less damaging than removing by temporarily 'fixing' the outer sprocket to the inner part threaded on the hub. Depends on the freewheel. Get some plus-gas on the stuck thread.
Lubrication is not my strong point..Grease? Oil? Groil? Heavy oil? light grease?
Yes they usually come greased, whatever that means, and it often seems to end up constricting the free movement of the pawls. Make an assessment of the strength of the springs and lubricate accordingly. Stong springs=much 'click' and pawl wear, but not so free freewheeling..use grease. Weak springs=not so much 'click' and pawl wear, but free freewheeling.. use oil.