Skyrim takes place 200 years after the end of the last game, Oblivion.
Because it takes place so far from the rest of the games in the series (both temporally and geographically), there are few characters or locations that are relevant to any of the past games.
That doesn't mean that Skyrim has nothing to offer the stalwart Elder Scrolls fan, though.
The Dark Brotherhood, for instance, a player-joinable group of assassins-for-hire, returns in Skyrim, as do the Daedric Princes (or at least minor shrines devoted to them, manned by their followers.)
Even Alduin, the big-bad of Skyrim shows up in the lore of previous Elder Scrolls games, though the rest of the empire thinks he's the Aedra Akatosh. (He's actually his firstborn son)
If you're looking for a general history of Tamriel, the realm in which The Elder Scrolls takes place, the UESP has you covered there too.
But most of that is ancillary to the game itself. Skyrim was not designed as the 5th game in an ongoing series, but as a game able to stand on its own two feet. Even if you've never set foot on Nirn before, Skyrim will welcome you into its lore all the same!
Basically, what you can do is go under the main menu, select the magic tab and click Active Effects. If you currently have a disease, the effects will show up here in red (connoting a negative effect). Here are the diseases that you can contract in Skyrim as per the Elder Scrolls Wiki:
Ataxia: Lockpicking & Pickpocket become 25% harder. This disease is contracted from traps and Skeevers.
Black Heart Blight (Dragonborn DLC only): Drains 10 points from carry weight.
Bone Break Fever: -25 Stamina. Contracted from Traps, Bears.
Brain Rot: -25 Magicka. Contracted from Traps, Hagraven
Droops (Dragonborn DLC only): One-handed and two-handed weapon damage is 15% lower. Contracted from Ash Hoppers.
Rattles: Stamina recovers 50% slower. Contracted from Traps and Chaurus
Rockjoint: 25% less effective with melee weapons. Contracted from Traps, Wolves and Foxes
Sanguinare Vampiris: -25% health, progresses to Vampirism. Contracted from Vampires
Witbane: Magicka recovers 50% slower. Contracted from Traps and Sabrecat.
Lycanthropy: Transformation into a Werewolf.
Best Answer
They will wish the floor. Child labour!
I experienced back talking from some children, this just happens. In the case of back talk, they won't do anything.
Knocking things is, as @Ben mentioned, a poor collision detection.
Source:
http://www.uesp.net/wiki/Skyrim:Adoption