Use a power bank instead of batteries for a LEGO train
6xAAA means the motor needs 9V, right?


Give or take, yes. The nominal voltage of a AAA battery is 1.5V, so 6 in series is 9V nominal. In practice AAA's are more like 1.6V fresh giving the lower bound of the motors max voltage rating of 9.6V. Furthermore a typically AAA battery terminal voltage is around 1.3V or so under load for most of its capacity, so the motor should run fine at 7.8V, albeit slightly slower.


  When using rechargeables they only supply something like 1.2V, so the motor is slower? Or are the batteries empty more rapidly? How does that work?


With the lower voltage (7.2V), a simple brushed DC motor will simply run slower, possibly to the point of stalling. It really depends on the motor whether or not it will work. You are unlikely to damage anything by using rechargable batteries in this application.

From experience, LEGO motors will run off rechargable batteries OK.


  I want to use a power bank that has fast charge ability (ie supply 9V) and hook that up. How do the AMPs play into this?


I've split the last paragraph in two as the questions are distinct.

You will need to find out what the current draw of the motors is to be able to determine how much current your supply needs to be capable of delivering. There are three ways of doing this, one is experimental, one is guesswork, one is research.


Use a current meter in series with the motor when powered from your AAA batteries to measure how much current it uses. You will want to apply some load to the motor (e.g. pressing it down on the LEGO track) as the current will increase when the motor is doing more work.
Make an assumption about AAA batteries. A typical AAA battery can't really maintain more than ~1A continuous (don't confuse this with the rated capacity in mAh). Based on that, as long as your power supply can provide at least 1A of current you will likely be fine.
Find somebody who has measured it. For example, experimental results here show the current draw is around 160mA with low load, going up to around 200mA or so under higher load. And that also shows a 9V lego motor tested at 5.4V. So as long as your supply can give lets say 250mA or more, you should be fine.



  And will that automatically switch to fast charge (9V, 2A) when the motor needs that?


This depends on what you mean by a fast charge power supply. 

If it is a simple 9V rechargable battery pack, then it will provide 9V by design.

If you are referring to modern mobile phone or laptop chargers (e.g. USB power delivery), then no. Such a charger will not switch automatically. They require some form of control (e.g. resistor values, or PD controller) to select a voltage. 

You would need to find out what your power supply uses to select the voltage it uses, and implement whatever is required to switch it to supply 9V.