Can I trade four of a kind to the bank on my special building phase?
No, you can only trade with the bank in your own trading phase. The special building phase is just for building!
No, trading with the bank even with your ports (2:1, 3:1) is not allowed. If that rule did not exist, it would be very unlikely to have more than 7 cards in your hand.
Taken from the rules (http://www.catan.com/files/downloads/settlers_5-6_rv_rules_100107.pdf):
• Special Building Phase – Your opponents may build as outlined below. The Special Building Phase occurs just after the end of your turn (i.e., between player turns). All the other players may participate in the Special Building Phase. Each player then takes his turn clockwise around the table, and is allowed to build anything he can create with his resources. 3 Note that no player is allowed to play Development Cards during the Special Building Phase. Also note that players are not allowed to do any trading with other players—nor are they allowed to use Maritime Trade—during this phase. They may only use the resources they have in their hands. For this reason, players are advised to trade as much, and as advantageously, as possible with the current player during his trading phase. They will then have the resources they need to build during the Special Building Phase. The Special Building Phase is an opportunity for all the other players (who are not currently taking their turn) to build roads, settlements, and cities, and/or to buy Development Cards. This phase allows each player to influence the game, even though it is not his turn!
No, you may not trade 4:1 with the bank during the special building phase. As per the 5-6 player rule book:
Also note that players are not allowed to do any trading with other players—nor are they allowed to use Maritime Trade—during this phase
The 4:1 trade is defined under Maritime Trade in the base game rulebook:
b) Maritime Trade
You can also trade without the other players! During your turn, you can always trade at 4:1 by putting 4 identical Resource Cards back in their stack and taking any 1 Resource Card of your choice for it.
If you have a settlement or city on a harbor, you can trade with the bank more favorably: at either a 3:1 ratio or in special harbors (trading the resource type shown) at 2:1.
Note that no trading with other players and no maritime trade means that no trading of any kind can take place during the special building phase.
I'm not certain there is a definitive answer to this based on the rule book quoted above. The clause highlighted in the previous answer specifically prohibits "trading with other players," and does not specifically prohibit trading with the bank, as in a 4:1 trade. Had the game manufacturers intended to prohibit "all trading" then they would not have been so specific to prohibit just inter-player and maritime trade. Furthermore, it could be argued that since you can "buy" DCs from the bank then the 4:1 transaction is also a "buy" rather than a trade since it's between the player and bank and not between two players.
Perhaps this is just an unintentionally ambiguous translation from the original German (I think) rules or it's just poorly written.