Not sure I answer to all points because it is a rather large question.
Ground loop and impact on signal integrity
There is a ground loop as soon as you connect the USB cable between your device and PC - regardless of Class I or II AC-DC converter. The ground loop is completed by the AC-to-DC-capacitance in the PSU. 50 Hz current will flow through your ground. If you have any signals referred to your ground, this ground current will impact their integrity. If the signals are extremely small, it can become an issue. Even if you leave the USB shield unconnected, you still don't avoid this because the other USB signals are Earth-referenced if you connect them to a PC.
The right step to take here is to not allow precision signals to be single-ended. Period. If you have transducers or whatever that generate a "single-ended" output, then force them to be differential by using dedicated signal return traces for each of these signals.
ESD
Although the AC/DC converter can have isolation, that doesn't mean that ESD doesnt reach the Earthcurrent doesn't flow through them. There are capacitors of at least ~1 nF to Earth which the ESD charge will use for initial dispersion. But the charge cannot actually leave through this capacitor, so in the end it will flow down the USB cable, because the USB is Earth referenced as we have established above.
If the shield (low impedance) is connected, it will do so rather fast, and retain minimum voltage on your ground node. This is good, because it means that the USB signal lines don't have large common-mode voltages, which can upset communication or damage the PHYs. With the shield unconnected, you only have the signal lines, which is not a good scenario. The PC likely has ESD protection on these lines, so it may be still tolerable after all. However, the impedance on these lines is higher, so it will take longer for the strike voltage to disappear, which will leave your box at a few 100s V of common-mode voltage for that time. This is usually not an issue, but just saying.
EMI
There are two good ways to tackle macroscopic EMI in general: Tightly and solidly connect everything with low common-mode impedance to an EMI-ground (e.g. PE) or make all connections to said EMI-ground high impedance and make sure that the device is radiation shielded. That way, you create a local EMI-ground (e.g. chassis) that coherently floats on the external EMI-tides.
As you have many cables and varying external connections, the first scenario is somewhat hard to achieve. The latter case is also not trivial because you have cables to a PC for example. You have two low impedance connections to the Earth ground at high frequency: the Y-caps in the PSU and the USB shield. As discussed before I advocate leaving the shield connected.
In order to make these two interfaces high impedance for EMI, I suggest putting cable beads on both of them. USB cables often have them integrated. For your DC power, you can also find such cables (with barrel plugs) or clamp one on yourself.