Do not only look for “movement” when you see in used with the accusative. In is very versatile and has a lot of meanings that cannot be easily summed up in a few words. A good dictionary will describe them, such as Lewis & Short. Under “II. With acc.” look past letters A (“In space”) and B (“In time”) for C:
In other relations, in which an aiming at, an inclining or striving towards a thing, is conceivable, on, about, respecting; towards, against; for, as; in, to; into
This is the key to most of your examples. Let's look at them individually:
Pacta in favorem tertii
This means “contracts for the benefit of a third party.” Lewis & Short call this “of the object or end in view,” and other examples are: in gratiam, in honorem (in kindness, to show favor, out of good feeling, to show honor, etc).
In malam/bonam partem
An important and sometimes overlooked thing is that pars means not only “part” but also “side, direction,” so I would naively translate this as “in a good, bad direction.” But in reality it is a standing expression that refers to interpreting something in a good or bad way, so the dictionary meaning that fits best would probably be “like ad, with words expressing affections or inclination of the mind.” A particularly clear example is: paratus in res novas: Ready for new things. (In fact, you will often see the form ad bonam partem too.)
Par in parem not habet imperium
This means “an equal has no rule over an equal.” Here the other person is aimed at, one could say “has no rule against an equal,” except one does not say that in English.
In dubio pro reo.
For in dubio, no aiming, inclination, strife is in sight. Being “in doubt” is a static condition. This is why dubio is in the ablative. Reo is also in the ablative because pro takes the ablative and nothing else.