A few beginner's questions

[Sarin]

So, after a while of messing around Skyrim, some oddities popped up... so eventually I decided to ask about it here.

Random encounters, especially dragon attacks. I've had a few strange ones...

One. Shortly after Dragon Rising, I was messing around Riverwood, practicng my aim on various animals (was still very low level, and bows can be tricky on longer ranges for a beginner). I quicksaved, took a few shots at deer, they ran away...a few seconds later, I hear the roar, and dragon is here. Do not meddle in affairs of dragons, because you're crunchy, and good with ketchup. Quickload. Same scenario. I loaded a few more times, before finally realizing that I have no chance of defeating the dragon, so I tried fast travelling after loading. It worked. But a while later, as I was exiting Whiterun, I noticed a dragon flying around somewhere in Riverwood's direction (I have fade distance maxed, so it was quite far). I fast travelled to Riverwood, and found myself instantly in battle with dragon.

Second, was doing the Meridia's quest. Dropped off the beacon, and as I was up on the cloud, chatting with the Daedra, I noticed dragon flying some way below me. No sound, nothing that signalizes the encounter. It flew away in direction of Solitude stables. After I finished the quest, when walking away from the statue I was attacked by dragon. No idea if it was related.

Anyway, the point is... is it possible for random encounter to do something important without me seeing it? I've ran into already ongoing battle a few times, and probably missed a few encounters simply by going the wrong way. Can a dragon simply attack and ravage a settlement without me being there?

Second thing, horse management. I own one horse (Frost, from quest). Since I prefer doing my exploration on foot, and travelling with horse only when going inside the dungeon or from town to town, is it possible to leave a horse in stables and fast travel on my own without killing it?

Oh, and I had a weird bug. Bought Lakeview Manor, started furnishing it, had rats in the cellar. When I went outside, I had an aggressive Giant at my front door. He was probably [&@%!] at me because I started using his relatives and their herds as batteries recently.

[Aarah]

Anyway, the point is... is it possible for random encounter to do something important without me seeing it? I've ran into already ongoing battle a few times, and probably missed a few encounters simply by going the wrong way. Can a dragon simply attack and ravage a settlement without me being there?

Yes, things can happen when you're not there to see it. People can get killed by dragons, villages attacked by vampires, and other random things. This is why you'll sometimes come across dead npcs in town, or receive an amount of money that has been left to you in an npcs will.

Second thing, horse management. I own one horse (Frost, from quest). Since I prefer doing my exploration on foot, and travelling with horse only when going inside the dungeon or from town to town, is it possible to leave a horse in stables and fast travel on my own without killing it?

Your horse should never die, just because you have left it. It should be found at the stable you left it at, whenever you return, but if you fast travel to another town, you'll probably find your horse at the local stables there instead.
I've found that horses are usually safe if left in a stable, but if you leave them for a long period in the wilderness, they may wander off. They can hopefully be found in the stable that you bought the horse at (or where you got Frost, perhaps), but they may also get killed by something and you never see them again.
(Sometimes horses can even vanish for a while, if the game is feeling funny. I lost my horse once -it just disappeared when I left it outside a Dwemer ruin for a long period. I deemed it dead after looking for it at stables and not finding, but then it showed up at one of them a few months later. *shrug* Horses can be a bit odd. )

Oh, and I had a weird bug. Bought Lakeview Manor, started furnishing it, had rats in the cellar. When I went outside, I had an aggressive Giant at my front door. He was probably [&@%!] at me because I started using his relatives and their herds as batteries recently.

All the Hearthfire houses will get random aggressive characters spawning outside them. It might be giants, bandits, wolves, etc. You have to protect your home as they can kill your cattle, horses or even your steward, if you have them.

[Sarin]

Thanks. Looks like I'll have to pay more attention on my travels...

By the way, does quick shot perk affect crossbows?

[Aesir]

Oh, and I had a weird bug. Bought Lakeview Manor, started furnishing it, had rats in the cellar. When I went outside, I had an aggressive Giant at my front door. He was probably [&@%!] at me because I started using his relatives and their herds as batteries recently.

If you happen to want a pet skeever living in your basement you can. One of the three isn't hostile. Two of them will attack you, but the other one won't. If you don't attack it it'll just harmlessly wonder around the basement forever. Mine is named Skeeve.

I can't tell you how many cows and chickens I've lost to giants looking for an easy meal. I've even had bandits come in to my house on a few occasions. It sure gets chaotic and makes a mess of things when you have three or four bandits fighting me, my wife, Llewellyn and Vigilance in the main hall while the two kids are running around yelling "leave me alone."