Why is 1 satoshi the smallest division of a Bitcoin, and why is it important that 1 satoshi cannot be divided any further? Could there be a viable system where 1 coin can be divided infinite times?
One Satoshi is 0.00000001 Bitcoins. I think this is just an unofficial name for the smallest unit possible in Bitcoin. As far as the reason why a Bitcoin can only be divided down to 8 decimal places, I think thats just the way the creators set it up. I dont know if it could be changed at this point, but if so, it would have to come from the Bitcoin Foundation to make that determination.
The true reason for the smallest increment of bitcoin being 0.00000001 is not known, it was decided that this would represent the 'cent' , its like asking why dollars are only divisible up to the second decimal, it was simply made that way.
Can it be subject to change, it'd be very surprising, considering the amounts of satoshis available to the public (21 000 000 bitcoins having 100 000 000 satoshis each ) i don't even think that they considered changing it one day due to the very high amount of satoshis available.