Soo, how exactly does the "reduced one-handed penalty" work? Is the shown percentage reduced from 100% or something? I'm not sure.
When you're using two-handed weapon with one hand... there is a penalty and your accuracy is only 80% of whatever it was before... for example if it was 70% it would be decreased to 56%.
Reduced one-handed penalty means that the 80% penalty multiplier was changed for example to only 90% multiplier, or some other number higher than 80%.
Also, what does it mean when an outfit has a melee dodge penalty of 50% exactly?
It means that the dodge it has, for example 66% will be decreased by 50% when it is attacked from the rear, effectively being only 33% from the rear. On other sides than rear it will progressively increase, until it reaches 66% from the front.
Speaking of: If an outfit doesn't mention anything about melee evasion, does it mean that it cannot dodge, period? Just to check.
In general yes.
Check the "stats for nerds" to be sure (INFO button in ufopedia).
Lastly, how do ammo that does 125% damage to health work vs armor reduction? Is the remaining damage done after said reduction increased slightly then?
Yes.
PS: would be MUCH easier to answer your questions, if you gave an example weapon/armor for each point... there are many mechanics in the game... and I can only guess, which one you meant... so take my answers with care, because I may have answered different questions than you asked.