Tongera, I'm always a fan of alternate colonizers and colonizers in new places. Expect allot of that sort of thing TTL. As for your other questions:
1. That depends on whether you mean the effects of a moderately resurgent ERE, or of colonialism and Atlantic trade. If the former, then the effect is that the black sea is friendlier to Helenistic traders, and also that grain exports from the Crimea to Italy have shrunken on account of Byzantium taxing it to the hilt to get back at Venice. The latter hasn't had much effect on Black Sea trade. Sugar was never a big part of the trade, so Venice isn't affecting it with their adventures, while the Portuguese, although getting quite wealthy by sailing to India, are fairly insignificant in volume of goods moved compared to the landward trade along the silk road.
2. Not so good. Leftover rebels and brigands from the civil war are running rampant in Greece, although they aren't strong enough to pose a threat to the government, and piracy has grown in the absence of the Venetian fleet's protection, though not to a crippling extent.
3. Nope, and they'd probably be confused given that Byzantium is just another word for Constantinople. If they knew that its use meant that they were less than the direct continuation of Rome, then they'd be pissed. Their Empire is shrunken, but not their pride.
4. Emperor of China, King of France, Holy Roman Emperor, King of Castile, and Basileus ton Romaion (for Roman connections and associated prestige, not true power). Note that the King of Castile is more powerful than the HRE and possibly the King of France, but Castile is still considered something of an upstart with a history of mismanagement.
5. I'd prefer not to give too much away here, since colonialism will be responsible for a good many trade routes and major cities, but as for cities that have already boomed on account of trade compared to OTL, there is Antioch, Trebizond, Doros, Theodosia, Lisbon, and Syracuse.
ImperatorAlexander, Fear not, the next update will be filled with the Crusaders
cimon, Although they take some influence from them, the Charlotteans do not consider themselves Cathars. Of course, almost anyone who disapproves of them will make the connection, and attempt to use it against them, so it will all come down to who argues their point more eloquently I think.
Benedetto is a classic example of how history is more fun when its subjects are a bit chemically imbalanced, and that's all you need to know for now