(Pic 1) The "crack" at the top of the door and down the sides (are they the same type???),,,, they look to me as if someone has used a thick bead of acrylic filler or similar, and over time, it has pulled the top layer of plaster away at the the edges of the frame. Best way to repair would be to carefully remove all the old acrylic altogether, then repair the plasterwork back into the door frame. Worth checking too that the door frame itself is not loose!!
(Pic 2) The crack in the picture looks as though it has cracked at the end of the lintel.
For a "proper" repair for the lintel crack,,,, you would need to remove the plaster 4 or 5 inches either side of the crack, clean out the crack itself, repoint the crack, then cover the crack with some wire lath, and replaster over it. Sounds a lot of work, but it isn't.
(Pic 3) The corner crack down the mitre-joint in the coving, is just where the two pieces meet. It isn't what you would really call "a crack"!!! A drop of filler and a coat of paint will sort that one out.
For a quick fix, 2 ways,,
either rake out the cracks,, damp them down, then use a powdered filler to fill them up, ie, Polyfilla etc,,,
or,
fill the cracks, fibre tape them over,, then use "easifill" or similar to cover the tapes,, when dry,, sand down, then you're ready for decor. As i said, these 2 particular methods are only cosmetic ways to repair cracks,,, depends what you're looking for really.