1) I think you chose perhaps the least iconic view of Alhambra; from
other angles it looks much less like Palais des Papes. Note that the
in-game model also emphasizes the square courtyard and Moorish designs; IMO Palais des Papes would not bear any resemblance to the Alhambra in game.
2) Castles more or less look similar because it's a design that works, just like swords generally look similar. The design is practical.
3) St. Mark's Basilica is Byzantine, not Gothic, though the exterior was refurbished in Baroque style.
4) In terms of Gothic cathedrals, there are hundreds of great options; the real question is narrowing it down to
which ones do you choose. Nôtre Dame de Paris is probably the most iconic; Santa Maria del Fiore is fascinating but definitely pushing the boundaries of the already poorly defined category of Gothic architecture (and was finished well after the Gothic period--not an argument against its inclusion, simply an argument that it shouldn't really be considered a great exemplar of Gothic architecture); Cologne Cathedral (also finished after the Gothic period, however), Chartres Cathedral, Nôtre Dame de Reims, Canterbury Cathedral, and Westminster Abbey are some of the more spectacular examples of the style.
5) The list of Gothic castles is much, much smaller, Gothic being a chiefly ecclesiastical style. Palais des Papes and Krak des Chevaliers are probably the best examples; in terms of both historical significance and aesthetic qualities I think Palais des Papes wins out, though being the last surviving Crusader fortress gives Krak des Chevaliers some interest. Plus
chevalier is just a fun word to say...As for Heidleberg, the initial castle was constructed in the Gothic period, but the current ruins were constructed much later during the Renaissance.
