To be honest, I'm trying to understand how it would work just on the oracle.
I see two ways of it working.
Option A: An oracle has to use their arms in order to perform the slam attacks gained by the aspect. This means that using one arm for a different type of attack makes it so that they miss out on one of the slam attacks.
Option B: The slam attacks gained by the oracle are not associated with a limb of any sort and so these attacks are always available in addition to whatever the oracle is normally capable of.
The spell should come with similar limitations when applied to your animal companion.
Question 1:
Assuming option A is correct
No, it can either attack with a claw or a slam with that limb but not both. So its attack line is Bite, Claw/Slam, Claw/Slam
Assuming Option B is correct
Yes. because the slams are not dependent on any of the tiger's limbs.
Question 2:
ok, to start with if the tiger is initiating the grapple it doesn't get bite, claw, claw, rake, rake. It gets a single attack with a bite or claw of it's choice as well as 2 rake attacks. When it charges an enemy, pounce allows it to attack with a bite, 2 claws and 2 rakes. Otherwise the answer is much like the answer to question 1. When grappling it gets a single attack with either a bite, claw, or slam of it's choice in addition to 2 rake attacks.
Question 3:
The slams either are associated with the fore-limbs or they aren't associated with any limbs (depending on if A or B is correct). Because slams are natural attacks you can mix and match them with any other natural attacks you have that don't utilize the same limbs as your slam attacks.
Question 4:
It absolutely gets Slam, the only part I'm not clear on is if the slam attack requires the same limb as it's claw attacks. My inclination is that they do (meaning option A is the correct answer).