Manor were only 3.4 seconds off Hamilton who was pushing relatively hard though I don't think close to max, where as they were just over 7 seconds behind both at China(first dry qualifying they attended last year) and Abu Dhabi. So they've gained more than anyone which isn't even remotely surprising. The engine itself is worth the majority of that as 2014 Ferrari engine was a dog and they've switched to the 2016 car. But I wouldn't underplay the chassis improvement, not epic chassis or anything but you have to build a package that can actually put that much extra power down without just breaking, having the traction and downforce to apply the power and be that much faster. The still appear slowest but they appear close enough that they might not be a lap down after 15 laps, they might actually nab points in lucky races and they might actually compete a little with the slower teams, particularly if they get good starts. They actually had some pretty good starts last year much like Mclaren and were sometimes 5-6 places higher after the first corner but pretty much at the back 2 corners later. This year a good start and they might have enough power to hold their position and fight.
The field as a whole is dramatically closer.
Ferrari to Merc... impossible to say. LAst year at Australia they somehow were like 1.4 seconds behind Merc in qualifying but they were that much faster than Merc in Singapore iirc(close anyway). They were major outliers. I can't be bothered to work out the average but anything from 0.2-1 second behind, probably about 0.5 on average at a guess. I don't think the gap at Australia will be representative for the season as qualifying pace changed pretty dramatically track to track. Sometimes Ferrari 0.3 down and Williams nowhere, sometimes WIlliams 0.2 down and Ferrari nowhere.