Yea the stock browser has flash lite if I remember right.
And about updating no you don't have to but its going to keep bugging you until you do..I think if OTA 2.1 gets pushed, it notifies you like every 15mins until you upgrade. I would suggest going with 2.1 root..You'll have total control over your phone...like themes, apps you can't have without root and a couple other things that will be coming in the future.( after HTC releases the source for 2.1.)