Tachometer for my bike

Do the IO ports have internal pull-up or pull-down resistors?

Yes, they have both - and they're switchable with software - simply use pinMode(pin, 'input_pullup') and connect the contact between GND and the pin, and you're done.

Am I right that I can use also my Espruino Pico to do the first tests

Yes, absolutely. Stuff like setWatch and pinMode are identical.

Are there any major differences between Pico and Puck

Not in terms of how you write the software. Just define the pins you're using as variables right at the top of your code (var REEDSW = A7;, etc) so you can swap the pins over, and you should be sorted.