Where should I connect the switched power supply?
I'd suggest that you solder onto the back of the connector... See the next point...
connecting the battery to VBat would circumvent the fuse, right?
Yes, it also means that if your battery voltage is less than 5v (which a LiPo will be) and you plug it into USB you'll end up over-charging the battery (even without the charger IC), which could be very bad news.
MAX1551 ... Doesn't that mean that the board will always be on during charging?
Yes - I think you'd have some trouble switching it around so you could keep the Espruino off while charging.
Is there a specific reason you're worried about the Espruino being on? When it's in Deep Sleep it draws virtually no power (0.03mA) so there's actually not much of an issue keeping it on and having a 'soft' power button.
Thanks for that hint, maybe I should think about a soft power button then. I hadn't considered that yet, because it might drain the battery.
But that could also mean that I have to switch power for peripherals with a transistor since they might drain the battery much faster than just the Espruino in deep sleep.
Yes, it's true, you might need to switch peripherals. However when charging I guess it's unlikely you care about power draw.
There's a good page on FETs by @DrAzzy that shows how you can solder SMD ones onto the proto area relatively simply... That might work well for switching peripherals.
I want to connect a LiPo battery and a power switch to an EspruinoBoard 1.4. I don't want to use the JST connector. Where should I connect the switched power supply? To the GND and VBat pins of the board? Or to the back of the JST connector?
As I understand the documentation, there is a fuse between the battery connector and the VBat pin. If that is the case, connecting the battery to VBat would circumvent the fuse, right?
Another question: if I solder a MAX1551 to the designated position on the board, I understand that I can charge the battery through the USB connector. Doesn't that mean that the board will always be on during charging? Otherwise the switch would have to be inserted AFTER the charger chip...