I also couldn't quite figure it out, if Hungary places a district across a river but more than one tile away, does it get the production boost?
No, it has to be directly touching the city center.
This makes settling river bends very very handy...
Although you probably shouldn't ruin great city placement just to take advantage of the bonus on an extra tile. The key perk is that it applies to districts
and buildings. A single building is often more expensive that the district it's in!
I think the general consensus is that Hungary are - still after their nerf - a great civ for warmongering.
Probably the strongest warmonger on the larger maps.
As you both remark to
@Deadly Dog there is a very good reason Hungary was nerfed. Does Hungary always get a great map? No. But the issue is that the original raven king had no counterplay.
Imagine a mirror map. Hungary copies your moves exactly. But, if you haven't suze'd or conquered every CS within reach by the time you tech iron working, hungary
could get 3 envoys in one of them (as simple as meet first/quest+amani,) levy, and suddenly have an army of three or four 41

, 4

swordsmen before you've even built an iron mine. PLUS they still have been mirroring your military with their own regular army. By making it cost
something, it prevented the cheesiest version of this strat by forcing hungary to at least have some iron, or later strategics, which gives you a chance to deny them.
If there's anything one should pick up from gilgamesh and nubia's places at the top of every ranking, it's that it's always better to have your cities+someone else's than just yours. Pearl of the Danube or not- you don't need to use all your bonuses to play the meta effectively.