RE: casting flies
There is no lower limit on the size of the fly you can cast on a particular rod. From a casting perspective, consider a leader with no fly- it casts just fine. So I could take my 10 wt with a 7X tippet and cast a #32. The upper limit for rods/flies is another story for another thread.
The challenge comes in fishing with and catching fish on tiny flies I wouldn't want to use my 10 wt for fishing 20's let alone 32's. It is stiff as a poker in the tip and there would be no flex on a run. If that is actually the question you're asking, then it always will come down to how the rod flexes and how soft your wrists are, but yeah a soft-ish 4 wt should be able to go down to the tiniest flies with no problems.