I would contact the building department in your city and ask to speak to a plans reviewer. You might need to contact a professional engineer if your design exceeds the requirements of the Building Code. And please....get a building permit.
Soffit vents help with air intake into the attic while the ridge vent will help ventilate the air to the exterior. You will get air flow with both vents and will avoid ice dams. Hope this helps.
Most pre-engineered joist/beam suppliers have software available for downloading to use. As a structural engineer I am comfortable in using it but most homeowners should contact the supplier and ask that the member be sized. They will do this at no cost usually.
Sawcuts are only useful in forcing any concrete cracks to occur in the sawcut thus making the cracks less visible. Regardless of difference in slab thickness it is a good idea to 'tie' the patch into the rest of the slab. How far apart did you space the rebar?
These brackets are indeed available. You may however be asked to submit an engineer's report as these details may not be listed in your area's building code.