Going straight up would be a little more effective but, yes you can make a 90 degree turn. Each 90 turn is equivalent to adding xxx feet of ducting but that shouldn't be a real problem with a powerful hood.

Caveat - I am not a plumber - I think the general venting scheme may be acceptable, considering the relatively short distances. However, is that capped 3" pipe where the toilet used to be, or am I missing the toilet drain in the pictures? The angles for many of the pipe connections look like they could be a problem. For example, for a 3" toilet drain pipe you want gradual bends (45 degrees, etc.), especially when its close to other drain connections that would be plugged if it went the wrong way. I think I would want the sink drain to enter into the top half of the 3" pipe, like you would if it was a dry vent. This keeps the connection up high where it is unlikely to be blocked. Wet vents are normally kept open by flowing water, but with that close toilet connection I would be concerned that sewage could backup the wrong way and block the sink drain/vent. Bruce

Actual plumbers, and not "drain cleaners" do know plumbing code and how to properly vent things. You don't need an architect or an engineer for most residential plumbing work. You do need someone who knows code - at minimum. I've been the GC on a ton of residential gut jobs and never needed an engineer or architect - but I did need good trades people. Again, you came here wasting everyone's time with an unintelligible question and nothing specific like a diagram. You got exactly the right answer - the first one right out of the gate. And then you want to insult us and be an ass. Good luck with your plumbing job - because nobody wants to deal with your nonsense and your attitude.

It depends on the route and local labor costs. Cutting a bigger hole, is hard to do neatly. Call a HVAC pro.