I'm confused with the various websites and advice on this. I want to use 3×18650 cells (3.7V, 2200mAh each) connected in series to supply my device with +-11V. To charge them, can I just connect my pack to a 12V DC power adapter (2A), or do I need some additional components?
You can not.
First off batteries need to be charged with current limiting. If you just give it unregulated access to current the batteries will get hot and potentially catch fire.
In addition to that a series arrangement of batteries must be balanced charged so that no one cell is much higher than the other. A danger is that even if the average voltage is within the acceptable range one of the cells might be higher and get overcharged which can make it, you guessed it, catch fire.
Such arrangements of batteries need a proper balance charging device that has access to not just the + and - at the end, but also taps between each battery in the form of balance leads.