Your itinerary looks good but it is a little ambitious. One night in La Fortuna really isn’t enough time to experience the area, so you might want to add on at least a day there. As for when to rent a car, you’ll probably want it for the first part of the trip for La Fortuna, Rio Celeste (very remote area so a car is really necessary), and Monteverde (more spread out so nice to have a car). There are no rental car agencies in Monteverde so what you could do is drop it off in Quepos when you get to Manuel Antonio. You don’t really need a car there because everything in MA is along one main stretch and there’s a good bus and cabs are cheap. And you definitely won’t need a car for your time in Drake Bay. Make sure to check the difference in price for keeping it for your 7th day in MA because I think rentals are cheaper if you do a weekly rate (as opposed to daily). The drive from La Fortuna to Monteverde shouldn’t be that bad in Feb. since it’ll be the dry season- and the views are gorgeous so it is definitely worth having a car. Just get a 4×4 and you’ll be all set.
Answer for When to rent a car?