Some screws are still available. I usually look the parts charts for the machines up then either Google the part number with "Singer" or "Simanco" or I look in the inventory list from the supplier I use here in Canada. In most cases, I can get tension screws, I think I lost the latch spring from the FW bobbin case and managed to get a replacement - that was probably an alpha sew replacement, but the spring is completely surrounded, so I didn't think it would be a problem. I have a screw showing up today for a lady for a 78-3. Most of the really common screws should still be available - the 31-15/20 Bcases, the 15 Bcases, 221/22/301 Bcases etc. ETA: The tension springs too. I've ordered them for the 401 cases, the 15 cases, FW cases, etc.
I keep the screws in the ziplock baggies that most of my parts are sent in. Then they all live in a parts drawer organizer. If I "part" a bobbin case, I usually just mark it with a sharpie and throw it in the same bin. If it's a good case, I put it in with its corresponding bobbins in another drawer.