The 2" size you posted for the lav (bathroom sink) drain diameter doesn't make sense. Measure again or explain something more. A sink is usually 1.25", and can be 1.5" pipe diameter. Diameters cannot be increased forever, there are upper limits on these. How did you end up with a 2" on a lav?
It's a bathroom, so distances are small, but the tub is worrisome, if anything. Your tub can be drained with a pipe of a 1.5" diameter, or you could use a 2" pipe. Smaller diameters = less distance allowed. Larger diameters = more distance allowed. Maximum distances apply to trap arms: you need to measure the tub's trap arm length and post that.
The length of your 3" drain is not my biggest concern. (A toilet can be drained on a pipe going a long distance, under IPC based codes.) IPC and UPC based codes are all there are. Local variations (Ontario or Mississauga) will not have changed the pipe sizing and distance limits; local variations in codes deal with other stuff (e.g. like materials, like whether to allow homes to have supply lines made of CPVC). In the spirit of helping, I'll tell you that you appear to be learning as you go and not to know enough to be able to describe things well in the first place.