Can a 18650, 3.7 V, 2200 mAh battery be replaced with a 18650, 3.7 V, 3400 mAh battery?

Nominal 3.7 Volts.
2200-3400 mAH depends on chemistry and other factors..
List of battery sizes

List of battery sizes

No it would not be advised to go for a lower mAh as your phone would not perform as eficiently and also too I would recommend to replace it with same as qriginal 1.2 v -Ni-MH battery . And you can get any battery from Amazon .Com at avery good price, that is my go to place if I want something specific.

Contact your local retailer/service center directly or online here: Rose Electronics Contact

The battery will have a part number. Simply enter this into a Google search.

No it doesnt.. It just means that the battery can hold a larger charge.. I.E. the laptop will run longer then one with a lower mAh..

A higher capacity battery should work even better because a fully charged 900 mAh battery allows the phone to operate 50% longer than a 600 mAh battery between charges. I have had good results with Rayovac Recharge Plus 900 mAh in my Philips SE450. This phone will latch and not operate upon ringing if it doesn't like its batteries (probably high internal resistance), even though the batteries test good on a battery tester.

Hi,
You can replace current battery 800 mAH with higher mAH, but make sure the voltages are really same so that, you still can use your charger and the new battery will not damage your phone.
Regards,

Sony Vaio VGN-FZ38M battery

Type: Li-ion

Capacity: 5200 mAh, 8800 mAh, 10400 mAh,

Volt: 11.1 V

Size: 209.90 x 47.50 x 20.40 mm

Color: Silver

$ 89.33
http://www.daily-battery.com/sony-vgn-fz38m-battery.htm

NiMH batteries. You can use the larger mAh AA. It has more capacity and should give you longer service before needing recharge. The battery manufacturers recommend that you do not mix the batteries. i.e. don't use mAh 2100 and mAh 2500 as one set, use all 2100 or all 2500 as one set.