yes, just get a hole puch. You also could get a hole punch plier but i doubt is has enough reach.
Try this one from YunSheng
Pursuestar Silver Windup YunSheng Musical Mechanism Movement DIY Clockwork Music Box (30 Songs Option) - You are My Sunshine https://www.amazon.com/dp/B0862BR6NM/ref=cm_sw_r_cp_api_i_AA57F1X8JNDF323TWGPQ
Custom music boxes with the pin drums are incredibly expensive, sadly. Your best bet is the more affordable paper music box like this.
https://www.amazon.de/dp/B078S43GB5?ref=ppx_pop_mob_ap_share
You should check availability where you live. I got this one for myself and it works really well. The gears are made of copper so that should be fine. The tuning one the highest on lowest tone are a small bit off, but you will probably not use those in an interval together
It would be on just one strip, yes. Most likely you will have room to spare, but if somehow you go beyond the limits of the one strip you can tape in a new one.
This will allow all of the notes you need.