You can activate Figure of Fable's abilities regardless of what creature types it currently has. Each ability checks Figure of Fable's creature types when it resolves. If Figure of Fable doesn't have the appropriate creature type at that time, the ability will do nothing. (Go figure.)

Figure of Fable's abilities overwrite its existing creature types. For example, once Figure of Fable's second ability resolves, if it was a Scout when the ability resolves, Figure of Fable will be a Kithkin Soldier. It won't have the Scout creature type.

None of these abilities have durations. If one of them resolves, it will remain in effect until the game ends, Figure of Fable leaves the battlefield, or some subsequent effect changes its characteristics, whichever comes first.

The effects from Figure of Fable's abilities overwrite other effects that set power and/or toughness if and only if those effects existed before the ability resolved. They will not overwrite effects that modify power or toughness without setting it (whether from a static ability, counters, or a resolved spell or ability), nor will they overwrite effects that set power and toughness which come into existence after they resolve. Effects that switch a creature's power and toughness are always applied after any other power- or toughness-changing effects, regardless of the order in which they are created.