Would depend on existing roof structure. It would be quite difficult to do if it has a truss roof as you'd be cutting the bottom chord.... Not ideal as the truss is an engineered member that relies on the parts working together. If its a conventional cut roof then there is the possibility of doing it. Still a bit of roof framing work beforehand before cutting the ceiling joists. Personally you'd have to be pretty keen for the higher ceiling due to cost which no doubt could make it uneconomical, although it could look pretty good once done. As noted get it checked and estimated first. $250 per room is nowhere near the required amount....I'd expect another zero on that figure....

If you are confident in repairing the crack in the ceiling by yourself, then you need to purchase spakfiller from a hardware shop. Fill the crack, let dry, rub back with sand paper, and repaint ceiling. but it all depends on how large the damage is. https://www.bunnings.com.au/selleys-180g-spakfilla-rapid-gap-filler_p1231864

Is there a particular reason you want to lower the alfresco height ? If I had to make a choice , I'd almost prefer to go for 2.7 indoors , 3 metre alfresco , because thats where you want that open feeling , the luxury of space and height , moreso in in an alfresco . As far as being noticed , the only time it wouldn't be too noticable ( IMO ) is if the alfresco floor was lower than the house level -- if you step 'outside' through a standard or sliding door , and the roof feels lower , I suspect you would notice it . That , afterall , is why you go for a 3 metre inside height , to feel open and spacious .

The door should open onto a landing not step down. Can you extend the floor at the upper height.