Okay, I have a big house, so I fill it with a carl, a steward, a bard and 2 kids. All is well (aside from us all being autistic aside from the bard). I have a horse, a cow and 3 chickens. After a hard day, I come home to find bandits have broken in, killed the bard and upset my nicely arranged furniture. Reload. I come home and find the bandits outside. I kill them, but then cannot find the kids. Reload. Reload. Reload. The best outcome I can manage is 3 dead chickens. The steward (Onmund - don't get me started on that circlet I won for him) won't offer to replace them. Sooooo, I want my chicken back!!!!

Peripheral problems:

1) I cannot give one of my kids any gifts - the options are grayed out

2) The bloody horse follows me everywhere (I suspect there's no cure for this)

3) I'm going to test out Vorstag and Marcurio in a couple of dungeons to assess how bearable they are as potential husbands (superficial, I know, but they are the only 2 who look good enough as far as I'm concerned) but I seem to have misplaced the Mara necklace

Incidentally, I may throw Sanguine's rose off a cliff. The bloody thing will not stay put if I try to exhibit it.

For the bandit and other issues of that nature (you're using one of the Hearthfire houses aren't you?) there's a mod called http://www.nexusmods.com/skyrim/mods/41579/?for Oldrim; and http://www.nexusmods.com/skyrimspecialedition/mods/1936/? for SSE. You should be able to have your steward buy more chickens I think....

I can't help you with your chickens, but for the horse problem, the simple solution is to summon Arvak, ride it for 5 minutes or so. You'll see that there won't be any horse following you.

As for potential steward, i use Mjoll (Aerin comes with her as well, so you'll have a more populated manor). I keep Rayya as housecarl.

Sanguine give you the staff because you travel all around Skyrim. He doesn't want his staff to be forgotten in a corner of your house like a cheap decoration.

I think the option to give gifts to kids gets grayed out after you've already given a gift or two recently, but should return later once you stop being so charitable. I'm fairly sure it does that so people can't sit and stack up 'charity' buffs all day long. If the chickens are dead body types and not just missing and presumed dead, then you should be able to re-purchase them from your steward, although it might take waiting for a day or so for the dialog to return.