As fas as i know that airport was the main reason to make to develop the shortfield performance kit for the 737NG which became standard equipment on the -900ER and an option on the -800.
It is a short field, but it shouldn't be a big problem as long as the correct procedures are used.
Yes, that is correct.
As others have said, it's mainly used for short haul (up to about 300 nm), but the main route is to Sao Paulo's downtown airport, with nearby alternates in each case, so no need for lots of fuel, thus landing and take-off weights are much lower than for more conventional operations. The -300s which were used originally on the route were incapable of landing in the wet (when it rains in Rio it really rains!) and had to divert to SBGL.