i just put in new speakers yesterday so while its still fresh in my mind...
the rear door panels are held on by 2 screws (one by the inside handle to open the door and one by the part you grab to close the door) and theres also a small screw lookalike clip at the latch end of the door panel at the top (you have to gently unscrew it with a phillips until its 1/4inch sticking out and then just pull on it and it'll pop out.
the rest is just clips so you have to use some force but they will come off and once they are off just slide the panel up and out.
as for the electrical connector the tab that has to be pressed is at the bottom right in the middle, its really small. at the same time as pushing it in and pulling on it if you can get a small flat head to help pry it out it'll make it easier.
fronts are almost the same undo the 2 screws (theres no plastic screwlike clip on the fronts) then you have to remove the door lock /window switch parts by pulling up at the end toward the rear of the car and then pulling back once its popped out. theres another screw under that and then same deal with the clips and sliding up and out the panel.
oh and for both front and rear the trim ring around the inside door handle has to be removed too. you have to pry it out with a flathead screwdriver very carefully. the clips holding it in are strong so its easy to break
as for the small plastic piece that broke it could be a panel clip or a piece of anything really i'd need a picture to identify it.