1) price comparison between HK, US and SG
Cannot comment on this.
2) With bare eyes can you see the color differences? compare D To I.
Side by side you will absolutely see the difference. However, that will not be visible in say a D next to an E, but likely D next to an F, and most definitely a D next to an I. On their own, unless you are color sensitive it is unlikely the AVERAGE person will notice the color unless they were REALLY looking for the warmth. My personal "sweet spot" is an H.
The biggest difference is going to be in stones with cut quality differences. You will notice a difference between a well cut D and a poorly cut D, and in Tiffany you will find poorly cut stones, you have to look at numbers--find the cheat sheet in the FAQ thread and look at stones that meet the numbers.
3) The lifetime warranty what exactly is covers?
Cannot speak to that. My understanding is that it really only is a "guarantee" that it is what they say it is. Not that it's going to cover a loss or damage. I have found that polishing of platinum and gold is free depending which store you go to. Cleaning is always free but I do not trust the SAs to not damage my ring--I've watched how they handle those, and frankly, I'll do it myself at home.
4) it does not have GIA or AGS certificate, can we bring the diamond to get it certified elsewhere? Whats the cost?
Unless you have the stone removed from the setting, you cannot get the stone regraded by GIA or AGS. Both labs grade the stone based on weight. Unseating that stone making it no longer a single "intact piece" is detrimental to the value of the piece, I highly recommend that you DO NOT do that. It is simply not worth it because it will devalue it and risks the safety of the stone because you're weakening the prongs removing and reseating that stone, AND it will not look the same if you do that.