LiaThistle
Not technically true. You can "lump sum" it, or one at a time the payment.
Why? Because there's an odd corner case where you have something in play - let's say a Mire Boa ( G: Regenerate 2/1 ), and a Pestilence (B: ~this~ deals 1 damage to each creature and player). You could: pay BBB all at once and regenerate the Boa just once, or, pay BB and B and regenerate the Boa twice, or, pay B, B, and B and regenerate the Boa three times.
Yay for Murk Dwellers rules, no?
sweatdrop
This is not true. Pestilence has an activated ability with a cost. Every time you pay that cost, an instance of the ability is put on the stack. Objects on the stack resolve one at a time. Thus, it will always be dealt in 3 packets of 1 damage, and require 3 regenerations. It's possible you were right pre sixth edition, but things haven't resolved in batches for over a decade.
Assuming you are in fact still used to the old rules, I think you should know that tapping a creature doesn't remove it from combat, and artifacts with static abilities still work while they are tapped.