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1.No
2.No
3.He can fly if creatures can normally fly in a low oxegen atmosphere but might have issues breathing.
It clearly states what you can take. Size or shape of creatures are not one of them.
Beastform Mutagen
At 3rd level, a beastmorph’s mutagen causes him to take on animalistic features—whether those of an animal, a magical beast, an animal-like humanoid (such as a lizardfolk), or a monstrous humanoid. For example, when the beastmorph uses his mutagen, he may gain a furry muzzle and pointed ears like a werewolf, scaly skin like a lizardfolk or sahuagin, or compound eyes and mandibles like a giant insect. The beastmorph also gains his choice of one of the abilities listed in the alter self spell, which persists as long as the mutagen. He may select a different ability each time he creates a mutagen.
This ability replaces swift alchemy.
When you cast this spell, you can assume the form of any Small or Medium creature of the humanoid type. If the form you assume has any of the following abilities, you gain the listed ability: darkvision 60 feet, low-light vision, scent, and swim 30 feet.
Improved Beastform Mutagen
At 6th level, a beastmorph’s mutagen grants him additional abilities and options. The alchemist gains his choice of two of the abilities listed in the beast shape I spell, which persist as long as the mutagen. He may select two different abilities each time he creates a mutagen.
This ability replaces swift poisoning.
If the form you assume has any of the following abilities, you gain the listed ability: climb 30 feet, fly 30 feet (average maneuverability), swim 30 feet, darkvision 60 feet, low-light vision, and scent.
Greater Beastform Mutagen
At 10th level, a beastmorph’s mutagen grants him three of the abilities listed in the beast shape II spell, which persist as long as the mutagen. He may select three different abilities each time he creates a mutagen.
This ability replaces poison resistance +2, +4, and +6, as well as poison immunity.
This spell functions as beast shape I, except that it also allows you to assume the form of a Tiny or Large creature of the animal type. If the form you assume has any of the following abilities, you gain the listed ability: climb 60 feet, fly 60 feet (good maneuverability), swim 60 feet, darkvision 60 feet, low-light vision, scent, grab, pounce, and trip.
Grand Beastform Mutagen
At 14th level, a beastmorph’s mutagen grants him four of the abilities listed in the beast shape III spell, which persist as long as the mutagen. He may select four different abilities each time he creates a mutagen.
This ability replaces persistent mutagen.
This spell functions as beast shape II, except that it also allows you to assume the form of a Diminutive or Huge creature of the animal type. This spell also allows you to take on the form of a Small or Medium creature of the magical beast type. If the form you assume has any of the following abilities, you gain the listed ability: burrow 30 feet, climb 90 feet, fly 90 feet (good maneuverability), swim 90 feet, blindsense 30 feet, darkvision 60 feet, low-light vision, scent, constrict, ferocity, grab, jet, poison, pounce, rake, trample, trip, and web.
Well, it could be clearer, since it refers to gaining "abilities," yet you cannot gain "ability score" bonuses...
Same confusion caused by "racial traits" gained from being a race versus "race traits" category versus traits from other categories that reqiuire a specific race yet are not filed under race traits.
Yeeeeeaaah....