I'm going to do my best to summarize the Sixers/Kings pick swap and Sixers future draft rights. The Sixers can't get the Kings pick in 2018. They get an unprotected Kings pick in 2019, they won't get the Kings' 2020 pick, just their 2019. The swap with the Kings can occur only if the Kings end in the top 10 in the lottery. As you noted, if it's outside the top 10, then it goes to Chicago and we can't swap.
Here are two examples of the swap:
Example 1: Let's say the Sixers end 11th in the lottery, Kings end 6th in the lottery. This is the scenario:
Sixers get - 6th pick
Kings get - 11th pick
Bulls get - Kings 2nd round pick
Example 2: Let's say the Sixers end 12th in the lottery, Kings end 11th in the lottery. This is the scenario:
Bulls get - 11th pick
Sixers get - 12th pick
Kings get - nothing
The Stepien Rule isn't restricted for a team's own draft selection. Take Brooklyn for instance, they won't have their pick this year or next year (it'll go to Boston from the Garnett/Pierce trade). However, because of a pick swap this year (Boston gets to choose the better of Brooklyn's and their own pick), Brooklyn still gets a first round pick, so they were able to trade their 2016 and 2018 1sts since they would get a 1st round pick in 2017.
They do and it's top 3 protected, it looks like the Lakers will have at worst a 45% chance of falling out of the lottery again this season (at worst from a Sixers perspective at least). Given Brooklyn's standing, it seems unlikely they'll overtake them.