No, it's only in the liver, from what I can tell from the science, not the gametes.
No, it would not depend on the sex of the baby, as the chromosomes that you're editing aren't X or Y.
Evolutionarily, the inheritance of genes is a far slower process than the medical advancements we make, so what I think we're seeing here is a chasing down of the low probability events. In that, most of the evolutionary pressure is coming from things like dirty water and bad food, but as we're solving those low hanging fruit, we have to go to lower probability events to make progress that feels equally important.
Also, if I am wrong here on the answers to the questions, please correct me!
If they could get complete delivery to the liver stem cells, then the change could be permanent, although this is making many simplifications.
Organs in your body usually keep some very old cells (formed in the embryo) around which act as parents for all the new cells in an organ. Any cell can only divide a limited number of times, so they typically maintain a "tree structure" where the old cells create children and grandchildren (etc) that then differentiate into the organ-specific cells that do the actual organ work.
If you modify only the differentiated cells, eventually they die, and are replaced by descendents of stem cells; if those stem cells didn't get modified, their descendents will not have the fix, and the treatment efficacy reduces over time.
Both eggs and sperm producing cells are created during formation of embrio. We could even define that these cells as "clones of you" that were created not much after your first cells were created, because your DNA, that undergoes changes in your organism is never given to your offsprings - it is DNA of your "clone" cells. Eggs are as you have defined - "very old cells". Most probably cells that are producing sperm also can be defined as "very old cells" as most probably sperm production does not function the same way as other cells, that are staying in organism and accumulate mutations.
Stem cells from other organs has absolutelly nothing to do with this. Unless you are refering to procedures of planting stem cells from one organ to another to help failing organ, as stem cells are universal cells, that are able to produce cells for any organ.
That‘s what I was asking: Baby females already have all the eggs they will ever have once they are born, right? Matryoshka doll style. While sperm is always (relatively) fresh.