Can a character who has improved targeting (ignores characters and hindering terrain) shoot someone who has stealth?

Yes. They only need to have IM: ignores hindering terrain. They don't need to have IM: ignores characters.

Ordinarily, yes. Remember, Stealth does not mean a figure is immune from ranged attacks; it means "When it is not your turn, hindered lines of fire drawn to this character are blocked." A fig with Stealth that has hindering terrain between herself and the targeter, or who is in hindering terrain, ordinarily has LoF to her blocked by the hindering terrain. A character with Improved Targeting (Ignores hindering terrain) can target the stealthed character because the LoF is no longer hindered. If also possessing (Ignores characters), the targeter can target through a friendly or opposing fig as well as through hindering.

I think you meant IT: ignores hindering terrain.

As an added tip if that character has Outwit, and the character you're targeting has Stealth through a power, you can counter his stealth with Outwit so that the rest of your team can see him as well.

Thanks for the clarification. I appreciate the time you all take and your knowledgeable responses.

One final note: Improved Targeting: Ignores Characters will not let you target a character in stealth, but it will let you target a character behind them!!