Inconsistency in property valuations and HKMC mortgage

I am trying to buy an apartment in a (new - 25 years old) walk-up building. Vendor and I have tentatively agreed on $5.2m. GIven that this is a two-bedroom, light and airy flat with a roof top in a desirable location, I don't think it's too much in the current market. BEA is giving me a valuation of $5.28m but other banks' valuations are much lower - anything from $3.2m to $4.8m. I thought I was okay because BEA was providing a valuation at asking price. However, I need to apply for an 80% mortgage through HKMC. Yesterday I was told at the bank that the HKMC will use their own valuation, not the bank's. The added complication is that the HKMC won't release its valuation until you have signed the S&P and make the official application. Questions that I have are as follows:
1) How can valuations vary so much from bank to bank?
2) What is the prejudice against walk-up buildings, even new ones, about?
3) How often are valuations updated? Given the current market, all the valuations I have looked at seem to lag behind the market which makes it very difficult to get a mortgage on any property.
4) Can one challenge the valuation the HKMC uses if it is less than the agreed sales price?
5) Why won't the HKMC tell the vendor their valuation so they can make an informed decision on whether they will be able to finance their purchase before they sign the S&P?
6) If a bank is happy to value a property at a certain price, why would the HKMC deny that valuation?
7) Are there any other ways to finance the possible shortfall between what the HKMC might approve and the selling price?
Any advice would be appreciated.