I'm using the standard Raspberry Pi 3 to make some prototype products, but don't need the USB or Ethernet ports.
1/ Is it a good idea to remove them manually? 2/ If not, is it possible to buy custom RBP's where the only difference is that they don't have those ports?
I wouldn't attempt to remove them manually. You can see YouTube videos of it been done successfully but I reckon the guys have the right tools (and they don't say how many they have ruined).
element14 have a customization service. Minimum order 5000 units.
There are other boards (e.g. the NanoPi Neo Core, Duo or Air boards) that ship without any headers soldered on especially for this sort of scenario. Support is far sketchier than with the RPi, but if you can figure things out, it will greatly simplify what you're trying to do.
A RPi 3B without Ethernet or USB sounds like a quad core Zero. Is that what you're essentially after?
Yes, it is possible to remove USB and ethernet ports from a Raspberry Pi 3B and 3B+ if you have experience removing electronic components. Those are not surface mount but through hole components and are removable with tradtional methods. (Soldering iron, solder sucker, desoldering wick, etc.)
OR, you can buy a Raspberry Pi 3A+ which has no ethernet port and only one USB and is physically smaller. The down side to the 3A+ is it has half the RAM of the 3B/3B+. Everything else is the same as the bigger versions.
So if your project can live with half a gig of RAM that would be the way to go.
If you're new to soldering and do decide to remove the parts yourself I would highly recommend getting some experience on something already broken. In my youth I spent hours desoldering components from broken VCRs.
Be very careful, whatever your experience level, not to disturb the tiny surface mount parts on the Pi. They are much, much harder to repair than non-surface mount and require special tools and magnification.
