Every figure here is calculated from the deck rather than quoted, so the numbers and the reasoning stay in step.
Most of them are more common than they feel. Being dealt a pocket pair happens once every seventeen hands, which is roughly twice an hour at a full table.
You flop a set with a pocket pair about one time in eight. That single number is the whole argument for calling a raise with a small pair — you need the pot, or your opponent's stack, to be big enough that the one time in eight pays for the seven times it does not.
Flopping two more of your suit happens about one time in nine, and then you still have to hit. A suited hand is worth roughly three percentage points more than the same hand offsuit — real, but nothing like enough to justify playing every suited card.
Quads with a pocket pair on the flop is one hand in 407. At a home game that is once a year. At a table running four hands a night for a decade, somebody at your table will have seen it a dozen times, which is why "I have never seen that" is weak evidence about anything.
About 1 in 221, or 0.45%. Any pocket pair is about 1 in 17.
Roughly 11.8% of the time — about one hand in eight — holding a pocket pair.
About 35% from the flop to the river, and roughly 19% on any single card.