Yes, this is possible.
As you pointed out, you could implement the interface to the USB host using a USB to TTL UART interface. You would still need a microcontroller in-between to set up the pairing etc. with the other Bluetooth device. So you can't just connect the UART directly to the TX/RX leads of the Bluetooth module. Because of the serial interface, you may be limited to as low as 115,200 bps, certainly no higher than 1 Mbps, which is not even as fast as the slower USB 1.1 rate of 1.5 Mbps.
However on the slave side, you will need to implement a USB host to talk to the slave USB interface. This is not trivial. There are quite a few chips that implement a hardware USB slave interface, but far fewer that implement a hardware USB host interface. On top of that, you will have to implement a USB stack. If you want to be able to handle connections to USB hubs, its even more difficult. Depending on the microcontroller you pick, you might be able to get a library to help with this, but plan on spending a lot of time getting it working.
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.
Best Answer
Yes, special USB receptacles have been defined within Power Delivery specifications. In version 2.0 an extra special contact was defined, for both USB 2.0 and USB 3.0/3.1 Type-A connectors. They were called "PD Standard A Connector", and there some protocol is defined as well.
In Power Delivery Rev 3.0 all Type-A and Type-B connectors are "depreciated", and the focus now is on Type-C connector.
Going forward, it might be challenging to find the original "PD Standard A Connector" with extra insertion detect contact. Wurth Electronics makes one for USB3, and Assmann, both are still available at Digi-Key.