I noticed that my USB chargers have different output levels (400 mA, 650 mA, 1000 mA). Does that affect lithium-ion batteries at all or can they control the input level themselves?
Those are the maximums for the chargers, the device should regulate the charge and require only that the charger can deliver at least that. A standard USB1 / USB2 port can deliver 500mA A standard USB3 port offers up to 900mA A charging port may allow more. There are standards for charging ports - on a normal port, the device should follow USB signalling conventions, request 500mA power and wait until granted. On a dedicated charger with no data signalling the data lines are shorted, an 500mA is guaranteed at 5V, with voltage dropping as maximum load reached, The device, not the charger, is responsible for controlling the charge
Most lithium batteries can take more than most chargers can output so it just means the smaller the output the slower it will charge.
