Makes the door close easily

Your description indicates the door hinges require adjustment. Usually the striker would be removed and the door hinges adjusted for easy closing and equal gaps. It is likely in your efforts to make the door flush with the front wing, mudguard or fender, the hinges are too far in. Most likely your replacement door is not identical to the original - not unusual for various reasons... Once the door hinges have been adjusted to provide a satisfactory position and closing the striker would be refitted and adjusted so it goes into the catch or latch dead centre - neither lifts nor pulls down the door as it closes. That is where the door needs to be and if it stands proud a little it is just bad luck - often the front fender can be repositioned and then the bonnet or hood readjusted. A competent panel beater would be able to tweak things for you to make them acceptable. It might have been better to fit a new latch to the original door.

You will be needing to find a helpful body shop and ask them to either adjust your hinges and latches, or, replace parts that are broken.
God bless your efforts.

There must be a way to get the inside panel off. Then you could see and work the handle levers. From the handles to the latching mechanism, small rods work them. They attach on both ends. You will be able to see how the handles trip the latch, then grab the right rod and pull or push it in the right direction to open the door latch. You can do it, hard to describe w/o seeing one, but all work similar. Little rods, that's all you need to know. Uh, well, getting the door panel off is the biggest hurdle. Several screws, some may be hidden, be patient, plastic pin type fasteners along the bottom and up the sides of panel have to be popped out-usually one about every 4-6 inches. Once you get it loosened up, you will easily find the rest of the attaching points. Lift the panel up from the window channel and away. Peel the plastic ("waterproof barrier") film off carefully. You will want it to get a good reseal when you are done. Now you can see the inner parts, and how the handles operate the latch.
Once opened, spray with a penetrant, check the door sill all around, check for visible reasons it stopped opening. Sometimes the rods get stretched or bent, and the handles won't work. Good luck, big "do not slam" sign on that door, okay?

The back latch is electric release. It's a fuse under the dash. I forget which one, but it's not the door lock fuse. Just pull everyone and you'll find it.

Here's how I repaired mine. Go inside and remove the plastic 2" square plastic cover. By pushing on the lever inside this area, the latch will release. Push on the door at the same time, when the latch is pushed. With the door open, remove all four screws from the plastic panel. Now pry carefully the big plastic panel off the door. There are plastic snaps holding this on, all around the edges. Now there is another metal cover over the latch mechanism under this panel. Remove this. You now can see into the latch area and put the handle back into the slot where it came out of. You'll see that the ends of the handle can be put back on the round bar, but to hold them in place, I attached 2 nylon ties on one end. You can also purchase a metal push on retainer from the local hardware store. Mine has been repaired for 8 months and had no trouble. Ford used no retainer on these handles and after prolonged use, they bend and the handle can be pulled off. A twenty minute job. Your wife can even do it.
Fred C