FAQ for
Hard Boiled (1992) More at IMDbPro »Lat sau san taam (original title)

Apparently it's the Wyndham Teahouse, a famous Hong Kong restaurant where patrons are expected to arrive with their pet birds. (Would appreciate an update of the FAQ by anyone with more info.)

Besides the theatrical version there is another, about 6 minutes longer Taiwanese version, like a 'first cut'. Mostly, this runtime difference results from additional material at the beginning or end of many takes (but not only action scenes). Sometimes, there are completely new or alternative takes. In rare cases, something entirely new has been added. A detailed comparison between both versions with pictures can be found here.

The suspension of disbelief is necessary here. Both guns he uses in the tea house gunfight are Norinco copies of the Russian Tokarev TT-33 which only had an 8-round magazine. We never see Tequila reload the pistols, however, firing "two-gun" style is a mainstay of many John Woo films & adds to the invincibility angle of the character, also a mainstay of many Woo films. So, yes, it's completely implausible but still fun to watch.