Power a circuit off USB the correct way
You are approaching the problem upside-down.

First, all BC/QC etc. charging protocols are used primarily for DEVICES, so the devices can understand the source capability, and then configure itself internally to align their consumption with the source. There could be another stage to negotiate the voltage level, but this in this case both provider and consumer must use the same protocol/standard. 

The ANKER powerbank is just a source of 5 V 2.4 A. It doesn't even follow any announced standards. Their "PowerIQ" is utter BS. 

(Disclaimer: there used to be ideas of intelligent chargers that are supposed to change advertised standard, and select the "best" based on maximum current draw. The problem is that phones also use some intelligence and take different charges depending on the battery's state of charge, so the algorithm doesn't converge. These "chargers" might work a bit better than the dumb ones, but no guarantee).

Therefore, if you have the Anker powerbank, you don't need to do anything, just split the power as you suggested yourself.

Regarding your specific qiestions, 

(1) No, you can't be sure that any USB (legacy Type-A) port will let you draw 1.5 A. While usually you can do much more than that, some ports may have current limits set for 500-600-900 mA, so the port will sense overcurrent and will be shut down; [A 100% USB standard-conforming, protocol-following port with 1.5 A capability must be specifically designed as "charging port", and shall be explicitly labeled as such.]

(2) Yes, if a bank is rated above 1.8 A (say, 2100 mA), you can safely draw 1.8 A from it without any fancy reservations;

(3) Since this is a case when you don't need to do anything, the question is moot. But no, Pi-3 or whatever can't handle any of the "negotiations" even if the bank follows one of intelligent charging standards. First, the power supply port on Pi doesn't have any connections to D+/D- pins. Second, to bring in negotiations, you would need a special IC that is designed for this.