Gideon's second ability causes him to become a creature with the creature types Human and 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 Human and Soldier are just creature types (not planeswalker types).

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

The set of creatures affected by Gideon's first and third abilities is determined as the abilities resolve. Creatures you begin to control later in the turn and permanents you control that become creatures later in the turn won't get +1/+1 or +2/+2.

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).

All creatures you control get +1/+1 from Gideon's first ability, not just the ones that it untapped.

If damage that can't be prevented is dealt to Gideon after his second 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 has indestructible, if Gideon has no loyalty counters on him, he's put into his owner's graveyard.