I was in Dubai last week.
1. Canon lenses have an international warranty so you'd be OK. It's only the cameras that have localised warranties.
2. No. You need a UK receipt.
3. Not that much cheaper. Some Sigma lenses, however, do seem to be a fair bit cheaper in Dubai. For example I picked up a 120-300mm f/2.8 for £1,000.
4. Sharaf DG in the Times Square mall is probably the best all-round camera store. Grand Stores Digital in Mall Of The Emirates is good for Nikon and Sigma (incl Canon-fit Sigma) but strangely doesn't stock Canon. Unfortunately none of the Dubai electronics shops have decent web sites, so comparing prices means a lot of leg-work (or more accurately taxi-work since you can't walk anywhere).
Remember that lenses bought outside the EU are subject to 6.9% import duty and 17.5% VAT when you bring them in. I paid that on my 120-300 because it's for the hire business and I have to be squeaky clean, and it was still a bargain. Before you go shopping, you might want to consider how honest you feel. The chances of being stopped at Heathrow are pretty slim, but you will cop it big time if you are caught.