There is no standard for standard part numbering of fasteners. ASME B18.X only defines thread forms and sizes. That's why we use ".250-20UNC" as the part number in our BOM. The description would be "Socket Head Cap Screw" or "Heavy Hex Bolt." This allows purchasing to buy a fastener that is a ".250-20 SHCS" from any vendor they like. If that fastener has to be grade 8, or meet a MIL-Spec, then we call that out as a specification and purchasing can by any ".250-20 GRD 8 Heavy Hex Bolt" from any vendor they choose.
We use vendor part numbers in our BOM because that is the part that the engineer or designer researched and will satisfy the design requirements. Whether or not material substitutions is allowed is based on company policy. When we use a vendor's part number (which makes ordering easier), we specify the vendor as a flag note. To limit the problem you issued above, a vendor no longer producing that part, we often provide alternate part numbers and vendors in that same flag note. Sole-source items are not good. The only problem is spending the time researching multiple vendors.
For you last question, I don't deal with electronic parts very often. Are you referring to connectors, cables, wires, crimps, splices, resistors?
For items like connectors, you are better off picking a vendor you like and using their part number with a thorough description of what it is you want. For resistors, capacitors, and other components, you can probably just spec out the size: 5 Ohm, 10 microFarad, etc.
--Scott
For some pleasure reading, try FAQ731-376