First, you should fully read the rules for Natural Attacks if you haven't already.
As quoted above, the maximum number of attacks your eidolon can make applies only to natural attacks. The rules for attacking with a manufactured weapons are distinct from making attacks with natural weapons. When combining the two, all natural attacks are treated as secondary attacks. Furthermore, you cannot use a claw or a slam attack that turn if you attack with a weapon held in the corresponding hand.
Iterative attacks with your manufactured weapons function the same regardless of if make additional natural attacks. For instance, if you had a primary bite, a greatsword, and +11 BAB, you could full-attack with the greatsword at +11/+6/+5, then attack with the bite as a secondary attack at +6 (If I'm not misremembering the order).
Yea Nat attacks I understand but it was just me not paying attention while reading. I might just revamp my Ediolion Knight concept an try a Mounted Summoner.... though do you know if I'd have an issue being in combat on its back while it fights? If anything It's just like normal mounted combat right?