I think I would have to have a discussion with the neighbor about the pig situation. In Texas they have that old saying "good fences make good neighbors". That may end up being the best solution to the wandering pig.
As far as the calcium supplement (oyster shell) the way you provide it to the chickens is more a matter of what works best for you.
The logic is; chickens know when they need extra calcium and will eat it when they need it. That is the premise behind the free choice method. In a commercial setting having it mixed in with the layer feed works because those hens don't do much if any moving around, being in a cage that is just large enough for you to sit in one place isn't good animal husbandry but it works for egg production in the commercial setting. It is not healthy for the hens, it is also going to shorten their life span, cause health issues and on and on, I do not approve of that methodology and think it barbaric.
In the end it is up to each individual to find a method of raising their chickens that meets with the needs, desires and health of the animals in the care of that individual. What works for some may be found to not be the best method for you. Yes you will get conflicting ideas of what method is best, that is one of the reasons there are so many methods out there.
On Buzzard's Roost, we practice natural husbandry of all our animals, it is our belief that mother nature gives each animal the knowledge of what they need and they (the animals) will eat what their bodies tell them they need, when they need it. Therefore, we don't mix an "all in one" food such as the commercial people do. We provide any supplement in a separate container, the chooks, take in what they desire and if they don't feel they need it, they don't have to eat it. We have fresh water, at all times (both water nipples and regular water supplies) available for them, natural foraging is their main food supply with enticement treats provided as needed or per our bedding down for the night regimen.
Confusion is easy to arrive at, There are many "experts" each with a different best method, the way to end the confusion is to make a choice and trial that choice to see if it is a best fit for you and your flock, herd, gaggle etc. If you are observant of your animals behavior, you can end up with a method of husbandry that makes you happy, your animals happy and healthy and in the end, you will be a good steward of both your land and your animals.