Hi @Anonymous
ad1 I think that in each steel design and concrete design codes are limits for maximal members deflection or displacements. In all codes I have used up to now there is section about displacements (SLS conditions) Please refer to your local steel design and concrete design codes.
ad2. In case of each roof segments i would define direction according to vector determined by middle arc points

Ad 3 You can use required reinforcement design procedure for shells. Please refer to Required reinforcement procedure
There are many tutorial for shell required reinforcement design on Youtube as well Autodesk Tutorials refer to webinair 5
Ad4
I would define pinned pinned connections for diagonals and chord ends. To reduce possibility of instability I would define releases for rotation around axis perpendicular to truss plane (If members are not rotated around its axis it should be RY-RY release. In 3D structure it is difficult to define stable structure using truss members so I would not recommend using them.

Krzysztof Wasik