I will not take the time if it was not you ^^
Correct, at the difference than it's the source of the P1 than decide it, not the generation of the seeds.
So in fact :
F1 Jack herer x F1 Jack herer = F2
F1 Jack herer x F1 White Widow = F1
F2 Jack herer x F2 Jack herer = F3
F2 Jack herer x F2 White Widow = F1
So F(n+1) when the initial P1 are the same only, or you restart in F1 with heterosis if it's not the case.
There is no limit in Filial generations. F9, F20, F30 ... must of the best ruderalis lines (Fedora, Futura, Felina, Compolti, Ferimon ...) have twos digits generations indicated after theyr name. So the famous Futura 75, is a F75. The potent USO 32 in CBD is F32 etc ... i quote industrial lines because they can't play. Most of IBLs are certified.
The Filial indication never disapear, even if you create a new hybrid. It's an important indication.
The S game is another domain than initially is not intended to leave the lab'. You call S1 an experimental cross of a dioecious specimen than you treat chemically to produce staminate (on a female) or pistils (on a male) and than permit to lock the genetic on itself. For different purpose : testing this exact phenotype as male donor but also to gain time in stabilization to have an overview of the genetical strenght, testing also a GMO engineering (to known if it finish fertile or not, useless mutants or not, by a "bug" in the genetical code).
In a perfect world, all valuable elite cuts will be S1 then widely distributed. But like i've said, it's an experimental process at the basis than can't reach a valuable quality grade as ouput. No one want to grow this offspring to earn his life in producing a competitive weed ^^
The feminized seeds is generally a kind of cheat of the twos process. In the industry at least, it's generally a mix between an F1 and an experimental S1. You can use a fully recessive specimen with near no footprint to be the "reversed"' pollen donor but also to outcross it with a basic one well know to produce a low average of herms in offspring etc ... always remember than if it was as easy than it appear in theory, all elite cuts will be less desirable than today. Everyone will be able to grow pure GSC, ECSD, Chem4, Trainwreck as a common weed like Skunk#1, Masterkush (oops), Jack Herer or White Widow.
BX or Backcrossing is simply the fact to cross a F(n+1) with one of its P1, generally to do what the S1 are not capable : preserving a specific specimen but in maintaining a decent level of quality. In simple word, to keep the weed the closer possible to the original.
But it is also used to correct a breeding mistake in selection between twos generations. So you can also operate a BX between the F3 and the F4 because your choice have generated a bad move (like i don't known, less trichomes in a breeding plan than is intended to increase it).
Hope it help ;o)