Yes, and yes. But, you might not like it.
A typical Fender neck width is 2 3/16" at the heel edge-to-edge. So, a 2 1/8" (2 2/16") spaced bridge only leaves you 1/16" to share between the two edges, putting the E strings within 1/32" of the fretboard edge. That's perilously close, and will often result in pushing or pulling the strings off the neck while playing. This is often referred to as "vintage spacing". "Modern spacing" at the bridge is slightly narrower, usually 2 1/16".
As for nut width, it rarely matters to playability outside of player comfort. Use whatever floats your boat on that end.