Sounds like two separate issues.
The DS likely is just worn. The entire latching mechanism can be removed. The escutcheon rings around the inside handle need to be compressed for access to the pin holding it to the mechanism post. The pin can be pushed out with a punch. Be certain to find the pin as there are indents that can mislead. The pins shouldn't need more than a few taps to move.
The inner door inspection panel needs to be removed. I have found it necessary to remove the glass from the regulator and the door. In my experience, the latch mechanism can't be retracted without this step. Your results may vary.
There are screws in the inner door by the handle and by the latch - remove these. There is also a screw holding the outer handle in place. Locate it by the striker on the edge of the door. Comparing your doors likely will show that this screw on the PS is missing. This would be a cause for the handle movement described.
Once all the attachment screws are removed, the entire latch assembly can be removed from the door through the inspection panel opening.
The typical wear points are the shaft opening (it wallows out of square) and the inner latch/locking contact points. Opening the cover to the inner latch is part of the issue. The tabs holding the whole business together will crack off without much effort. Repair of the inner latch/lock has been done by smarter folk than me. Welding and JB Weld are both approaches with success.
There are also repops that fit and work from Midwest Early Ford. Ultimately, replacements were my solution.
https://midwestearlyford.com/