Gideon's first loyalty ability causes him to become a creature with the creature type Soldier. He remains a planeswalker with the planeswalker type Gideon. (He also retains any other card types or subtypes he may have had.) Each subtype is correlated to the proper card type: planeswalker is only a type (not a creature type), and Soldier is just a creature type (not a planeswalker type).

If Gideon has 9 loyalty as you activate his last ability, he'll be put into your graveyard and won't be exiled.

A non-Gideon creature is a creature that isn't also a Gideon planeswalker. For example, Gideon's Company is a non-Gideon creature.

If damage that can't be prevented is dealt to Gideon after his first loyalty ability has resolved, that damage will have all applicable results: specifically, the damage is marked on Gideon (since he's a creature) and that damage causes that many loyalty counters to be removed from him (since he's a planeswalker). Even though he's also a creature, if Gideon has no loyalty counters on him, he's put into his owner's graveyard.

Gideon's first loyalty ability doesn't count as a creature entering the battlefield. Gideon was already on the battlefield; he only changed his types.

Any attacking Gideon creatures won't get a +1/+1 counter, but as long as two or more attacking creatures aren't Gideons, those attacking creatures each get a +1/+1 counter.

If Gideon becomes a creature the same turn he enters the battlefield, you can't attack with him or use any of his abilities (if he gains any).