Wow... it is actually recommended that mittens be worn till 6 weeks of age, so it is kind of late to be off mittens only now.
It is natural for babies to suck their fingers. Just let him be. Mine does it because I don't want to introduce a pacifier to her.
Non-nutritive sucking is very important to babies as well as this makes them feel comforted.
http://sg.theasianparent.com/are-pacifiers-really-good-for-your-baby/
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