For the back door, generally you loosen the sticker plate (the one attached to the body of the car, that the door lock grabs onto when it closes). To get a smaller door gap, loosen the stricker plate and push it IN towards the seats, then tighten it up very tightly and try it out.
For the front passenger door, sounds like you have a bad exterior door handle. Either something broke or a rod clip fell off inside the door. You should pop off the door panel and have a look see.