Roland MicroCube GX MOD: bluetooth aux in
Connecting the signal itself: Can I connect the output of the module (i.e., the R-G-L pins) to the corresponding pins on the built-in 3.5mm input jack? I guess this means that both inputs (the jack and the input from the bluetooth module) will be connected in parallel; is that ok or even safe?


It should be fine. My caution would be to check if the jack socket shorts the inputs to ground when the plug is removed. (This would be done to eliminate hum when nothing is plugged in and the trick is probably employed on the guitar input already.) I would solder onto the tip, ring and ground connections and check if it works. If not try inserting an empty 3.5 mm jack to force disconnect the ground contacts.
If you want to prevent a plugged in device fighting with the Bluetooth module then add a 1k resistor into the tip and into the ring leads.


Powering the module: the amp itself is powered via a AC/DC transformer that delivers 5.7 V / 2 A (so it says on the label). How would you go about taking just 5V from that? (as the module works between 3.5 V and 5 V).


Two options:

Use an LDO (low drop-out) voltage regulator (with the recommended decoupling capacitors).
Series connect a couple of silicon diodes between the 5.7 V supply and the Bluetooth module. They'll drop 0.7 V each. I'd check the open-circuit voltage of the 5.7 V supply though to see if it goes much higher than 5.7 V when unloaded. If it does the LDO solution would be less risky.