My 10 week old DD2 does this too but I don't think it is teeth, just part of their normal development at this stage ie discovering their hands and starting to explore by mouthing things. DD1 was exactly the same at this age but teeth didn't appear for another 2 months.
Teeth shouldn't make a difference to feeding. Don't worry unduly about that.
It's normal for them to mouth everything at this age. Their hands and their mouths have the most nerve endings, put them both together and they're fascinated. It has the unhappy side effect of making them drool a lot!
It can be teething yes but you'll notice more symptoms than just the mouthing and drooling.
DD and DS both did this and DD didn't have teeth until 12 months, DS not until 8 months.
No, it's not teething, it's a developmental stage when they are able to put their hands in their mouths. The drooling goes along with it because it's the body's defence mechanism to defend against them putting undesirables in their mouths. They drool so that what they put in their mouths dribbles out!
As others have said, probably not teeth. All my 3 did this from about 2 months - it was just that they had developed the motor skills to reliably put hand to mouth and they liked it. Another month or so and they were all enthusiastically sucking their thumbs. No teeth until 6 - 9 months for any of them.