1. yes it has a TU cost for falling, although it's a very strange one in the original xcom: 6TUs for falling down from 1 layer, but 0TUs when falling from higher - I did not implement this last one, it's just 6TUs per layer. The fall movement is not a real "step" it's TU costs are added to the horizontal step - if the total cost is higher than available TUs it will not allow to move.
2. I know openxcom does not have the same accuracy as vanilla - it has already been discussed about a year ago that the accuracy will depend on distance (we ended up with a gaussian distribution of an error in horizontal and vertical angle, but taking in account all things we know the original game does). But other accuracy calculations are not hard to implement if there would be a need.
There is no on screen indication - yet. But it is a good idea, because you might not always be aware of how much your hitchances are. I would vote for the percentage indication.
Also note : when testing openxcom now, you are probably every time testing with rookies with sometimes very low firing accuracy, as low as 40. It can make for lots of missing shots and very frustrating experience: don't blame this on the accuracy system