Shimano has a compatibility chart, 2017-2018 SHIMANO Product Information Web
It may be too strict; for example, the 9 speed rear deraiileur will work with otherwise 8 speed drivetrain.

I think the Deore front derailleur you mention is designed for 48-36-26 cranksets, and the M361 crankset is 48-38-28 (10T large to middle vs 12T large to middle difference). You can look at M391 or M591 crankset. M591 uses external bearings as opposed to square taper bottom bracket.

Since the parts you are looking at are all 9s I would also use 9s shifters and a 9s cassette.