Way to have multiple winners

As you've found, science stockpiles are not listed for individual cities, nor are they listed as an empire booster. The only location that seems to indicate that you have used a science stockpile is the Research Statistics on the Research Screen.

Using more than one science booster in a single turn will have apply the effect of one science booster each turn until they have all had an effect. This is shown below replaying 2 turns, the second time applying 2 science boosters on the first turn.

If you think you have more science boosters than will be needed for the rest of the game you can dispose of them in other ways:

1: Trade to another faction - this has restrictions as shown below

2: Sell your stockpiles on the market - at a rapidly diminishing price

I don't think you have to attack the "city center" tile itself to engage in an attack on the city - I think, as the hero standing there, that it would suffice to attack the borough tile, and that would initiate a combat against the city.

However, as you're suggesting there are definitely some serious bugs in their random-map-generator, mostly due to the whole way they've designed embarking, and the lack of water combat - which result in inaccessible strips of land trapped behind a single ruin/village - which is most problematic when it literally prevents you from doing a crucial quest (there will often be a minor-faction-unit stuck back there, sitting on a single tile you can't disembark onto because it's already occupied).

There's also just a general design flaw in the way that coastal edges of a city are not attackable - if you get a small city on an island, and perfectly fill the whole island, it's impregnable because there's nowhere to disembark.

You're not the only person to run into this - so if it looks like a bug hosing your ability to do something, it just might be.