Map Awareness
Riot has garnered some pretty effective videos with their Video Tutorial contest (Links posted below). As a beginner, you want to primarily focus on making sure you don't get ambushed by the other team (called a "gank"). While some of this involves Map Awareness, you also need to learn to not overextend, as well as keeping an eye on the enemies you're fighting in your lane. If you cannot see one or both of the enemies in your lane, let your teammates know!
Last Hitting
Killing minions and enemy players nets you gold to buy items. However, if you don't land the killing blow on an enemy minion, you will get ZERO gold, even if you've done most of the damage to it.
The faster you kill enemy minions, the faster the minions reach the enemy tower, which will make quick work of all non-cannon minions. It's better to keep the minion fights as close to the middle as you can; you only need to finish off the minion to get gold from it -- see if you can limit yourself to only attacking minions when you will kill them!
Tower Aggro
The enemy towers are dangerous. They have lots of health, armor, and a powerful attack that can quickly decimate low-level heroes. It's important, then, to know how the turret picks its target.
Enemy towers will always target allied minions first, switching to champions only if there are no longer any allied minions around. The exception to this is if you deal damage to an enemy champion, in which case the tower will immediately switch to the damaging champion, shooting at them until they die or move out of range.
Let me repeat that: If you deal damage to an enemy champion within range of the tower, it will immediately start shooting at you: You do not want this. Be very careful when attacking the enemy at their own tower.
Recommended Viewing
Four of these videos are a result of the Valoran Video Contest held by Riot Games, and are quick, 1-minute videos touching on just the basics (which seems exactly what you're looking for). The fifth video is made by Shurelia, an employee of Riot Games, and goes much more in-depth into what "Zoning" is, and how to take advantage of it.
Riot games have put a special effort into having balanced champions for this game style as well. I don't believe there are any champions to avoid. However, the team composition changes a bit.
AP Carry
You will still need one, or else the other team will just build against AD and will own you as soon as they are a bit stuffed.
Tank / Off Tank
King in solo holding the bot lane, also very good in "tower diving" (if we can still call it so in Dominion).
Melee Fighters
They tend to be the heroes everyone picks as they are sort of kings on this map. They deal quite some damage and have high sustainability (so they don't need to Back often), and are often very good in 1v1 (which happens pretty often in Dominion).
Ranged AD Carry
More than one is too much, but not having one (to have more fighters) is a handicap. He deals crazy damage and can attack out of tower range or defend minion waves without exposing himself in front of the tower. From the games I've played or seen, having only melee champs is clearly a handicap.
Support
I rarely see them in Dominion and believe they are overlooked. Each time I've had one on my team, it was awesome to hold the windmill (we never had to back, support would always buff/heal us).
However, having a support requires good team play, because the champion won't do anything on its own (compared to fighters).
General
As XP gain is so fast in Dominion, teams are usually built with mid/late game champions. Riot tried to correct this in a previous patch by lowering the XP gain aura on the map, however, you still get to level 6 tremendously fast, so don't hesitate in taking weak early game champs (like Kassadin, useless before level 6).
Try having a hero or 2 (at least) with high mobility (Rammus, Kassadin, Nocturne, Twisted Fate, etc.) to do lane swaps and be unpredictable in your tower attacks.
Conclusion
All heroes are viable. It all depends on the team composition.
Good Akali, Irelia and Xin Zhao champions can however be freaking awesome with their ganking abilities and life steal.
Best Answer
Sales are always announced the day before it starts. So other than that there is no warning.
Here is a list of previous sales. Searching for Ahri you can see she was somewhat recently on sale (April 5-8) which means she probably won't be again for a while.
This google docs spreadsheet is completely fan-made and theoretical, but predicts what future sales could be based on how long it's been since a champion has last been for sale. Can be a bit useful but remember, it's not official at all.