B-19 HOW IS CELL ABLE TO TELEPORT BACK AND BE IN PERFECT FORM?

First, the official explaination from Cell:

"Hehehehe........... You all seem to be very startled...

"Very well, I shall tell you... The outcome of the event is also a very fortunate miscalculation for me!

"Inside my head, there is a small, hard object; it is my 'core'; as long as the core is not damaged, my body will be able to regenerate. Luckily, during self-destruction, the core was not damaged.

"Truthfully, I never thought I would be able to regenerate... I was very lucky... What made me even happier was, although I no longer had Number 18 inside of me, I could still regenerate to Perfect form... And not just the normal Perfect form, but like Son Gohan, my power was significantly upgraded. This might be attributed to the Saiyajin cell, which provides a great upgrade in power after surviving a near-death experience!

"Plus, I also learned Son Goku's Shukken Iddou (teleport) technique! In other words, I'm back even more perfect than ever! Not only did Son Goku not defeat me, he became a great help to me!"

So, how was Cell able to learn the Shukken Iddou? He had seen it performed many times before, but never experienced what it felt like until he teleported with Goku. Therefore, all we can conclude is that he learned by experiencing (not by seeing, as it has been suggested).

Next, how can he be in Perfect form without #18? Does this mean that if he had been blown to bits with only his core intact before he had the chance to absorbe #17 and #18, he would be able to regenerate into Perfect form?

Not likely. My personal belief is that after he absorbed #17 and #18, the genetic coding was somehow registered to his core. The core was not working when he spat out #18, but was working during the total regeneration, and that is why he could regenerate back to Perfect form.