
Dragonchess Player |

Refer to page 90 of the Bestiary:
Bite - primary attack, 1.5 x Str bonus to damage
Claws - primary attacks, normal Str bonus to damage
Wings - secondary attacks, 0.5 x Str bonus to damage
Tail Slap - secondary attack, 1.5 x Str bonus to damage
Also refer to Natural Attacks on pg. 301-302:
"Primary attacks are made using the creature's full base attack bonus... Secondary attacks are made using the creature's base attack bonus -5..."

Dominigo |

You only get 1 x Str bonus on damage if its primary and 0.5 x Str bonus if its secondary. The only time a creature gets 1.5 x Str bonus to damage with a natural attack is if it the creature's only natural attack or if the creature has a specific exception in it's statblock. Since Form of the Dragon doesn't say that you get 1.5 x Str on any of those attacks, you shouldn't recieve that benefit.
As for which attacks are primary, the entry you should refer to is here. Primary attacks are made at your full BAB, while secondary attacks are made at BAB - 5.

Dragonchess Player |

You only get 1 x Str bonus on damage if its primary and 0.5 x Str bonus if its secondary. The only time a creature gets 1.5 x Str bonus to damage with a natural attack is if it the creature's only natural attack or if the creature has a specific exception in it's statblock. Since Form of the Dragon doesn't say that you get 1.5 x Str on any of those attacks, you shouldn't recieve that benefit.
Again, Bestiary pg. 90:
"Bite: This is a primary attack that deals the indicated damage plus 1-1/2 times the dragon's Strength bonus (even though it has more than one attack)."
"Tail Slap: ...A tail slap is a secondary attack that deals the indicated damage plus 1-1/2 times the dragon's Strength bonus (this is an exception to the normal secondary attack rules)."
The universal monster rules on natural attacks that you linked to specifically says: "Some creatures treat one or more of their attacks differently, such as dragons..."
Form of the dragon gives you the natural attacks of a dragon, so you use the rules for a dragon's natural attacks.