Can I reuse mods from found weapons? I always recycled the weapons, but it seems that I have to build every mod for every weapon from scratch.
Yes! However, you'll need to remove the mods or change them out for a different part at a crafting station, before you scrap or sell the weapon.
For instance, if you find an .50 Cal hunting rifle, and want the receiver, you'll need to replace it with a different receiver, which you'll need the availiable parts to make (or just to have a different hunting rifle receiver in your inventory/workbench). You'll then have the .50 receiver in your inventory as a mod that you can add to any weapon that it's compatible with.