Abilities that trigger when a permanent "becomes untapped" won't trigger if a stun counter is removed instead.

If a permanent has more than one stun counter on it, only one will be removed each time it would become untapped.

If a tapped permanent with a stun counter on it would become untapped, a stun counter will be removed from it instead. This is a replacement effect.

If untapping a permanent is part of a cost (such as that of Halo Fountain's first ability), you may pay that cost by "untapping" a tapped permanent with a stun counter on it. The stun counter will be removed and the creature will remain tapped. However, the cost will still be paid.

On the other hand, if untapping multiple permanents is part of a cost (such as that of Halo Fountain's last two abilities), you can't "untap" the same permanent more than once to pay that cost.

Stun counters are not keyword counters, and they don't cause the permanents they're on to gain any abilities. They won't be affected by effects that cause permanents to lose all abilities.

Stun counters exist independently of the effects that created them. If a permanent has no stun counters on it, it will untap as normal.

Stun counters replace untapping for any reason, including players untapping tapped permanents during their untap steps.