You can solder the switch more or less anywhere. One side needs to be a GPIO, and the other side can be GND, 3v, or a GPIO. The metal case of the Bluetooth module is also GND so you can use that if you need to.
There's no need for a resistor as you can use the chip's internal pullup resistors (shown in that link I posted)
Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
This might be some help: http://www.espruino.com/Pico+Buttons#software-external-button
2 of those 4 legs of the buttons are just shorted to the other 2, so can be ignored.
Yes, you can - or you can remove two on one side.
However if you search for
6x3mm tactile
you can find smaller 2 wire through-hole buttons like https://www.ebay.co.uk/itm/30x-Momentary-Tact-Tactile-Push-Button-Switch-2-Pin-DIP-Through-Hole-3x6x4-3m-Jt/123623523055You can solder the switch more or less anywhere. One side needs to be a GPIO, and the other side can be GND, 3v, or a GPIO. The metal case of the Bluetooth module is also GND so you can use that if you need to.
There's no need for a resistor as you can use the chip's internal pullup resistors (shown in that link I posted)