that board is super crappy. there are plenty of better and fairly inexpensive options available from pocket adventures, tinkerboy, glitch'd gaming, as well as others. the joystick on that is a cheap digital one and just wired to the same inputs as the d-pad. it would not take a psp stick easily (different wiring, as well as just mounting and positioning in that spot is not the same). personally, i think the analog stick on a zero build is overkill since it doesn't support any games/systems that actually need it, but if you really want it, just mount it using a 3d bracket - there are options for that on tinkercad and here in the forums too i think. be advised though, you would need another component to handle the analog input, like an ADC or micro controller.
i don't know anything about that boost board. it looks like it might work, but i've found that super cheap aliexpress stuff isn't always very reliable, and there is typically no support for it, so keep that in mind - you tend to get what you pay for from there.
the buttons and screen are ok. you'd get better quality ones from somewhere like retromodding or handheld legend, but those would work ok. quality ones do work and look a bit better generally, in my experience anyway.
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