A door is one of the most often used features of a house. Over time it wears and needs adjustments and repairs to it's closing surfaces. Weather stripping on entry doors are most often in need of replacement on the sides & top or bottom (door sweep). If you can put a piece of paper between the door and the weather stripping and slide it up and down with no friction when the door is closed then it needs adjustment. If it is torn or punctured then it should be replaced. The door sweep should prevent air movement under the door to the inside or visa versa.
The complete weather stripping barrier will stop energy loss and create a more comfortable room for the occupants. Energy Loss surveys usually pinpoint faulty weatherstripping as a major factor in air infiltration / heat loss in a building.
If the lock doesn't latch properly then you may be getting a poor seal on your door weather stripping as well.
Interior doors may bind for many reasons. One of the most common reasons is settling of the beams in the floors. This can cause one side of the door frame to be lower than the other. Another common reason is a build up of paint on the hinge side and near the door stops . This can cause the door to pull its hinges out and cause more wear on the hardware and frame. Change in humidity can also cause a door that used to open "perfectly ", to stick or bind as it is being closed due to shrinkage and expansion of materials.
A new replacement for your old wood door, identical to the old one, or in a new style that you choose can be custom made to fit.
If the original hardware is in good condition, then it can be reinstalled, otherwise, new hardware can be sourced to fit.
Repair any physical damage and remove all the coatings prior to re-sanding the door on both sides to make it look more like it did when it was new.
Refinish hardware if possible and apply new coatings to protect from the elements.
Install new weather stripping if needed and reinstall hardware, adjust if necessary.