If you got ridiculous with the salt I've have questions. But if it is a reasonable amount of salt, no issues. Sea gulls and some other salt water birds have a special gland that filters out excessive salt. Chickens don't have that gland so, just like for you, eating excessive amounts of salt is not good. But a little salt is good. It is not how much salt is in one bite but how much total salt they eat all day. So as long as it is in moderation it isn't a big deal.
Some people say to not feed your chickens milk products because they can't digest it. But others feed their chickens yogurt as a treat. Some people that milk goats or cows feed their chickens excess milk. They do this for years on end and it doesn't hurt them in spite of some people saying they cannot digest it. Even if they cannot digest it (I don't know if that is correct or not) you won't have enough milk in those eggs to hurt them, if it would hurt them to start with.
Some people feed pepper to their chickens or other animals thinking it will help with worms or other parasites. I don't know of any specific studies that back that up, I seem to remember a study with goats that said it did not. But in any case, it will not hurt them.
I would not hesitate to let he chickens eat those scrambled eggs.
Go right ahead... Those eggs are healthy for them. I usually make my scrambled eggs with water instead of milk because water makes the eggs fluffier than milk (my whole family is allergic to milk). Constantly giving them dairy is not good since it doesn't agree with them, but a treat with it once in a while is okay.
Chickens don't digest dairy well, and a steady diet of it will give them the squirts. I offer yogurt after a course of antibiotics to help repopulate the good bacteria in their digestive tract. I believe that the benefits outweigh the drawbacks.