Dying
DDI is a condition, part of which states that you are unconscious. Unconscious
DDI is a condition as well, part of which says that you can take no actions. Therefore you cannot activate powers unless they explicitly state that no action is needed.
The Death Saving throw is still a saving throw, you only fail if you roll under a 10. Rolling a 20+ is a special exception that allows you to spend a healing surge. Heroic effort can only be used on a failed attack or a failed saving throw. Therefore it could not be used in this situation. (I'd have no problem with a DM allowing it though, it sounds like a cool use to me). Note that it could be used on a roll of 9 or less (a failed saving throw)
Assuming the PC has successfully rolled below an 11 on the d20 to cast a spell, the spell takes their action on this turn. If it successfully dispels the spell, all effects of the spell are also removed.
An affected target's speed is halved,
This ends as soon as slow is dispelled. Since movement says you can move up to your speed, you are no longer impinged by this effect and any movement you might have left using your full speed can be used.
it takes a -2 penalty to AC and Dexterity saving throws.
This ends as soon as the spell effect ends.
it can't use reactions.
This ends as soon as the spell effect ends. Note that it doesn't say the PC doesn't have reactions, just that they can't be used while under the effect.
On its turn, it can use either an action or a bonus action, not both.
The PC has used an action on its turn to cast dispel magic. Assuming the spell is successful and it dispels slow, and the PC has a bonus action to make, the PC can now take that bonus action.
If they didn't roll below 11 then they are still affected by the slow until their next turn when everything stated above applies. In between these turns they are still casting the Dispel Magic which requires concentration: if that concentration is broken before their action on the next turn the Dispel Magic is lost and they remain slowed.
Best Answer
You take damage at the start of your turn.
You make a saving throw at the end of your turn, unless something or someone grants you a saving throw. For example, Boots of Free Movement which have the following power:
Note that you cannot cheat by delaying your turn. If you are slowed until the end of your turn, it will last until you take your actions. Here is an excerpt from description of delaying which contains some other loophole closing rules as well:
Also note the following about the "failed saving throws" (we didn't know this and it would have made a big difference last session):
Failed Saving Throw