Answer to "Manual PTO not engaging blades"You have an idler pulley that has moved out of place or is seperated/seperating. Very careful inspection will tell you. Look for NEW wear marks on pulleys. Check springs too. Good luck
Answer to "While cutting grass oil screwed out from mower"It has excessive ring wear. Double check the oil level but Im fairly sure the rings are gone on that engine. After running,shut it off remove dipstick and look for smoke. Thats exhaust gasses making their way back into the crankcase. Not great news.
Answer to "Is my Briggs & Stratton 6.75 engine series motor a 4-cycle or 2-cycle"4 cycle. 100% positive