You may be able to fix the top rubbing by switching out the screws into the jamb for longer screws. 2 1/2 to 3" screws should do what you need IF that is where the problem is. What I see in the picture is a small gap at the hinge to the door leaf. Depending on how the other hinges are stressed, you may be able to grab the knob the same way you do to make it easier to open, and while lifting, try to notice if the hinge moves to the door leaf. You may need to pull up more than normal to make it move, but if it does, the fix will be there, not necessarily at the jamb, although it does not rule the jamb being the problem just minimizes it.
A tip about screws into the jamb. The screws that are closest to the pin are line up with the drywall layer so those screws will be of no value, unless you angle them in to grab the framing, then the head of the screw is at such an angle it may bind on the other half of the hinge as the door closes, creating "hinge bind" a situation that will fatigue other weak spots or cause the door to stick again. The only place I use the long screws are in the hole or holes closest to the door jamb. Those you can run straight in and hit the framing with no problem. Any screw only needs to go into the framing by about 1' to 1/2" for good grab, it can be more in softer framing but in older homes with dense studs, you may even need to drill pilot holes.
The fix for the hinge on the door leaf side may need to be done with TLC. The wood available in this type of door is limited, about 1 1/4" to 1 1/2", so that set the length of the longest screws you can use, the longest being 2", since the tapered point can protrude through past the thickness of the piece in the door. This may be all you need to do to fix the top. I this does, then remove the middle hinge pin for now, to make ready for the fix at the bottom.
The gap at the bottom of the door is created by the jamb being bowed. The gap almost disappears at the bottom corner. It would be best to shim the jamb between the rough opening, but that would mean removing trim etc. A shim behind the hinge on the jamb side is a workaround. About the center hinge, something will need to done with that, maybe. By the time the top is drawn in with the longer screws and the bottom is shimmed, the way to tell what the center hinge may need is to remove the hinge pin and open a close the door to allow the hinge leaves to settle into there relaxed position. If there is misalignment, loosen the jamb side of the leaf, shim and tighten the leaf adjusting the shims needed to get both halves to line up, then drop the pin in. This should have everything nicely lined up, and all edges sealed.
As a mention, any screws you replace, use the same type of screw that came out, but longer, the gauge of the screw is important here. Also when it comes to screws for doors I dread the "split resistant" screws, they chew up the wood and destroy the full strength that the screws could otherwise achieve.