Pokemon-go – When does your pokemon get CP at a gym

The most likely cause of this is that all of the gym's slots are full, which means you will not be able to add another Pokémon until the gym is upgraded. Gyms can hold a number of Pokémon equal to the gym's level, so the gym in question is likely only level one, and its slot is already full. To increase a gym's level, you must win friendly "battles" (training) against the gym using only one Pokémon (as opposed to the usual six). Every time you beat a Pokémon at that gym, its prestige will raise, eventually leveling it up and adding another slot. At this point, you should be able to add a new Pokémon to the gym.

As Riley mentioned, the button will appear in the bottom left corner of the gym when there is an empty slot, and any Pokémon that you wish to place in that gym must be full health.

Yes, there are critical hits.

The critical strike rate depends on the attack itself.

See here:

    Items {
      TemplateId: "V0022_MOVE_MEGAHORN"
      Move {
        UniqueId: V0022_MOVE_MEGAHORN
        AnimationId: 5
        Type: POKEMON_TYPE_BUG
        Power: 55
        AccuracyChance: 1
   >    CriticalChance: 0.05
        StaminaLossScalar: 0.12
        TrainerLevelMin: 1
        TrainerLevelMax: 100
        VfxName: "megahorn"
        DurationMs: 3200
        DamageWindowStartMs: 2400
        DamageWindowEndMs: 2700
        EnergyDelta: -100
      }
    }

Or here:

    Items {
      TemplateId: "V0032_MOVE_STONE_EDGE"
      Move {
        UniqueId: V0032_MOVE_STONE_EDGE
        AnimationId: 5
        Type: POKEMON_TYPE_ROCK
        Power: 55
        AccuracyChance: 1
   >    CriticalChance: 0.5
        StaminaLossScalar: 0.1
        TrainerLevelMin: 1
        TrainerLevelMax: 100
        VfxName: "stone_edge"
        DurationMs: 3100
        DamageWindowStartMs: 1400
        DamageWindowEndMs: 1800
        EnergyDelta: -100
      }
    }