First, I am not a State Farm agent , I have an Independent Agency, we represent many companies.
Yes, usually “specific limitations” apply to items such as Guns, Jewelry, Antiques & Collectibles, Art, Silverware, etc. for Theft/Mysterious Dissapearence. Usually this is not the case with other perils such as wind, fire etc. Most companies are concerned about theft because fraud happens and saying your $10,000 worth of guns got stolen is pretty easy.
As for a auto/home discount etc. Items that are scheduled on a homeowners policy are subject to the same discounts you get on your homeowners. Most companies don’t usually give discounts on specific items that are scheduled on the policy. Hopefully that makes sense.
Yes, I recommend scheduling any items of value, usually it is pretty cheap depending on the item and you can get a smaller deductible. $1 per $100 is a very common price for scheduling items.