"P1 was really good, the auto was feeling great".
"I'm pretty pleased", said Ricciardo.
Even the normally inscrutable Raikkonen sounded upbeat.
"After a very positive morning session with both cars and drivers", said Allison.
The Ferrari driver's benchmark of 1:12.720 was the fastest ever recorded around Monaco's iconic street circuit and backed up pre-event predictions the Scuderia's auto would be best suited to Monte Carlo's unique twists and turns.
Schumacher, who won a record seven world titles and 91 races, also won at Monaco driving for Ferrari in 1997 and '99.
Buoyed by his win at the last round in Spain, having come back after an indifferent weekend in Russian Federation when he could not find the right set-up for his vehicle, Hamilton had been optimistic that Mercedes had moved further forward and were well-prepared for Monaco. "You need a couple of hours to undo that, more than a session would last so we made a decision to just push through and collect some data". Overrunning engineering works by the Ferrari mechanics meant he had to sit out the first 20 minutes of the afternoon practice. "It's been a bit up and down for me this year", Bottas said Wednesday at the Monaco GP.
"A lot of studying to do to find out where we went wrong, but I'm confident in my guys".
Monaco is the exception in the F1 calendar, with drivers getting a day off on Friday.
Mercedes pinned its Thursday struggles on a setup direction mistake, and Vettel is refusing to get complacent as he expects the German marque to respond on Saturday for FP3 and qualifying.
Mercedes had elected to run the supersoft Pirelli tyres initially, as their rivals went for the faster ultrasofts. Practice one was actually really good and we were the quickest, but then in second practice we just struggled to extract the grip from the tyres and we were sliding around a lot. "We're looking forward to a real fight".
Daniel Ricciardo converted his maiden career pole position into an early race lead despite heavy wet conditions - but his pit wall fumbled its way through his race strategy so badly it lost an easy win.
Meanwhile, Lance Stroll's miserable run continued.
Lewis Hamilton, six points behind after five races, was only eighth with a lap of 1:13.873.
Following the terror attack at the Manchester Arena on Monday night, British team Williams paid their respects with a #Manchester sticker on the front of their cars.
Vettel's optimism for the upcoming race was shared by his team mate.