Question 1: "Is it worth changing from 27 gears to a Shimano 3x10 drivetrain? I can imagine that the different gear ratio would make it easier to go uphill!"
BIKE: In principle, the new 30-speed drivetrains offer a finer gradation, but we only recommend them when buying a new bike. In our opinion, it does not make sense to convert the entire gear system just because of three more gears - but it is expensive. In most cases, the gear range of the new ten-speed drivetrains is no wider than that of 27-speed drivetrains. With Shimano, the range is even smaller than with 27 gears due to the changed gradation of the cranks (42/32/24 instead of 44/32/22). SRAM, on the other hand, retains the 44/33/22 gradation at the front. Even in the smallest climbing gear for hills, the new ratios do not provide a better gear ratio: While you cover 1.34 metres with one crank revolution with 22/34 (small chainring/big sprocket), it is 1.38 metres with 24/36 (Shimano 2011) teeth. Only SRAM's triple cranks reach 1.27 metres with a 36-tooth cassette.
Question 2: "Can a new 10-speed crank (Shimano XT FC-M770-10) be used with a 9-speed cassette, or does a 10-speed crank also have to have a 10-speed cassette and chain?"
BIKE: According to Shimano and SRAM, ten-speed components are not compatible with nine-speed drivetrains. However, our own practical experience has shown that it is perfectly rideable. Although the shifting quality suffers a little, nothing else should stand in the way.