What is the largest number of Settlers expansions that can be combined in one game?
There are 4 official expansions; which can legally all be used at the same time.

Seaside, Cities and Knights, and Traders and Barbarians can all be combined with any number of them being used or not used.

"Explorers and Pirates" does not combine as well, because it changes things more than the others in ways that conflict with the other expansions.

Cities and Knights comes with its own mechanic to replace development cards, so you simply do not use the development cards from the base game. The official FAQ has clarifications on how to handle things that only come up when combining expansions.

Note that both "Explorers and Pirates" and "Traders and Barbarians" are modular expansions, each with several different scenarios that use different mechanics. Some scenarios combine better with the other expansions than others. Catan.com lists each of the scenarios and how they work with the other expansions:

Traders and Barbarians combinations

Explorers and Pirates combinations