The first picture to me looks like your paint line cracked between the doors sile and the molding that holds in the pane of glass. Just sand it with a drywall sponge with an angle on one end and repaint. It cracked because someone did not cut out the paint line between the glass and the molding, wood expands and contracts glass does not.
I agree with the water damage in the second picture and you will always be fighting with that door because someone install the outside patio to high. There needed to be a min. of 4" from the threshold and the patio. There also needs to be a gutter over that area to reduce splash back.
If waters already wicked up that high and on the back side you can bet that there's more hidden damage to the door inside of it and under it.
What we do when we have to deal with this situation is replace the whole door as a unit. But this time the door gets sat in a sill pan, the door will be fiberglass and I order it with vinyl jams and vinyl brick molding.
The last picture looks like a cheap louon door that's delaminated. You can try patching it with Burmans Water putty or bondo, sanding it and priming and painting or just replace the whole door panel for about $25.00. If it was mine and I wanted to dress it up I buy a new prehung raised panel door for less then $75.00.