[RPG] When rolling a 20 for a Death Saving Throw, can you move and take Actions that turn

No,

Assuming the power used was Summon Thought Servant ^DDI, it works exactly like a Heal check.

Opportunity Action: Triggered when a dying ally adjacent to the servant starts its turn; targets the triggering ally; the servant makes a Heal check to stabilize the target or to allow the target to use his or her second wind

In a Heal check, the subject is told to stop making death saving throws. There is no option to willingly make them. In addition, the subject is still likely unconscious and cannot take any actions.

Stabilize the Dying (DC 15): If the subject is dying, the subject stops making death saving throws until it takes damage. Being stabilized does not change the subject’s current hit point total.

Note that there is no stabilized condition and being stabilized does not remove the Dying condition. The character is no longer required to make Death Saving Throws.

This means that a stabilized character is still a valid target for effects like Energizing Strike ^DDI and Get Up! ^DDI

The Dying condition is removed from the character only when the character regains hit points. Being stabilized is not enough.

Temporary Hit Points do not make you Conscious.

Rules Compendium p. 258 on Temporary Hit Points indicate that:

Not Real Hit Points: Temporary hit points aren’t healing, but rather a layer of “insulation” that attacks have to get through before they start dealing real damage to a target. Don’t add temporary hit points to a creature’s current hit points (if an adventurer has 0 hit points or fewer, he or she still has 0 or fewer after receiving temporary hit points). Keep track of them as a separate pool of hit points.

Rules Compendium p. 260 on Dying and Death indicate that:

Dying: When an adventurer’s hit points drop to 0 or fewer, he or she falls unconscious and is dying.

Thus, when a character is at 0 hit points or fewer (including the -1 in your case) they are dying (a status keyword) and when they have this status, they are also unconscious unless otherwise specified. There are certain powers or features that explicitly state that a character is not "unconscious while dying" but the rules for temporary hit points lack this qualification, therefore they do not undo the unconscious while dying effect.

The character will have -1 hp and 5 thp. The first five points of incoming damage will still go to the temporary hit points before the rest goes to hit points. This means if the character is stabilized they will no longer make death saving throws even if they take up to 5 damage (so thp are useful on dying characters). But the character still has less than zero hp, is still dying, is still unconscious, and must still make death saving throws on his or her turn until stabilized (thp do not stabilize a dying character).