From what I gather I have to buy a new horse every time mine dies? Lydia also died. I've read different things about her remains being in the Hall of the Dead in Whiterun or that a courier will show up to give you gold from her will? Neither of these has happened. I went back to where she died and don't see her corpse anywhere.

I wish there was an option to turn off friendly fire.

This is on the Xbox One version.

There is an "option" to protect Followers (does not apply to animals nor conjurations) from friendly fire. It is part of the Blackbooks of the "Dragonborn" Add-On. ["Winds of Change" is the title, it involves the Ebony Mine]

In my plays (15+) on the PS3, Lydia's body NEVER appeared in the Catacombs, I think that is a crome piece of the PC game.

Getting letters of inheirtance is kind of hit and miss. I have gotten letters of dead I never met, and not gotten letters of some I have.

Horses are something else altogether.

In my current play (just started a Special Edition game on the Xbox One "s") I have had two purchased horses begin to walk away from me, as if they were stolen/borrowed. I have found them in the Whiterun Stable. I had to kill them to finally get a horse to stay with me.

If you have the Dawnguard add-on it is worth the trouble to acquire the Ghost Horse.

The horse from the Assissina's Brotherhood is decent but has quirks. It gets jeuolose if you dare to ride another horse; so it will stay were last you left it. But, will physically disappear for exactly One Full Game Week after you have stopped using another horse; you must go back to the exact spot you had left it.

IT does regenerate when killed, back at the pond where it is first found.

Yes, you can buy, steal, or just take one of the few ownerless horses that are around if you want to. Also yes, that is true about followers remains going to the hall of the dead for whatever hold they are from. I believe the couriers only deliver notes of inheritance if the follower regarded you as a close ally, or lover/spouse (relationship rank 3 or better). If you use followers then it's always a great idea to go to Solstheim, go into Raven Rock mine and complete The Final Descent quest to get the Black Book: The Winds of Change. Completing the Winds of Change will get you a choice of reward ability, one of them is Companions Insight.. which is no friendly fire damage to followers in combat. Not exactly an on/off setting for friendly fire, but that function does exist through this ability and it works pretty good too.

edit: Ninja'd.. oh, and horses you own or have taken will return to where you bought or found them when they are not the last one ridden. Even hopping on another horse for a second will send your regular horse walking back home.