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Ideally, you want to keep the dual adjuster parallel to the stringer service, so yes, adjust both threaded adjusters equally...with the broken adjuster, it may be easier said than done.
for left right adjustment, the adjusters are fixed to the stringers. What you called the rod is formally called a trunnion. they to are 'fixed'. The engine/gear slids left to right on the trunions and the "nut and bolt" cause a clamping down action on the trunnion to stop further movement once adjusted.
You can correct the angular alignment of the engine to the prop shaft by articulating the dual adjusters on the vee drive independently, ie: if your shim stock is unequal from left to right, but equal from top to bottom.