please help, travelling with baby questions

Taking an international long flight next week and have a few questions:
The black bag is my diaper bag and the beach bag I want to take for my laptop, extra clothes etc. Is this ok as carry on?? 
Can I replace the beach bag with a school back bag? If that's even a better idea.
I need two bags with me in the airplane.
Can I take the stroller and car seat with me till I board? They'll put the stroller in cargo but will they take the car seat too? My son will sit on my lap. I have graco connect 
Any tips to keep in mind?