1) The crank and rear derailleur will work fine. The front derailleur may lead to some chain rub when in the big chainring/bigger cog and small ring/smaller cog combos because the 10-speed FD cage is slightly narrower than a 9-speed FD (10-speeds chains are narrower than 9-speed chains).
2) The flat-bar road front shifter uses the same cable pull as a MTB front shifter, which is different than the drop bar road front shifter. A flat bar FD is recommended, but a double chainring setup would be less finicky than a triple so you might be able to use the 105 FD. However, the FD will likely be the least expensive part anyway.
2. I use a flat bar shifter with a road 105 FD. The front shifter is a triple notch, but its only a double crank. I have a couple of gear combinations where it rubs, cause the shifter notches dont match the chain angles. I think its more a FD problem than a shifter problem. Maybe the 440 cages are a little wider to allow for chain angle overlaps without rubbing?
Which 105 FD and shifter do you have? An 8, 9 or 10-speed system?
We found out the new 105 10-speed cage is narrower compared to the 9-speed so we wonder just how much it will rub when using a 9-speed chain? And the 440 FD does have quite a wide cage and range respectfully but thought we'd ask just in case the 105 happened to work fine. Would be nice is Shimano made nice Ultegra grade flat bar FD's yea?
We did find something interesting though: Take a look at Shimano's web and download the flat bar FD-770-B double FD and the 105's FD-5600-B double FD drawing PDF and compare the two. They appear quite similar but Shimano says the new FD-770-B FD only works with the new SL-R770 shifters which may indicate Shimano's possibly leaning towards making flat bar FD's interchangeable with road FD's... Maybe, could be??? Would be great if they do...