The Orc Bloodline gives me the Orc subtype. Does that mean that I qualify for the Beast Rider feat?
Yeah.
Maybe.
Presumably so, since the faqs has specified that half-elves and half-orc may choose rules elements from their parent classes.
Yet, this might be a based on them having the elf blood and orc blood ability rather than the subtype, so the answer is not truly conclusive.
For what it is worth, the rulings on these subjects has been towards allowing rather than limiting options, for better and worse.
Any rules elements with race as a prerequisite work off the Type/Subtype system. So if it requires you to be a Human, mechanically speaking, it means you need to have, by some means, Humanoid(Human). This could be from being the Core race Human, being an Aasimar with Scion of Humanity, a half-breed race with Humanoid(Human, Whatever), or a custom race that is Humanoid(Human) but modeled differently (similar to how Drow are Humanoid(Elf)). So a Human with Orc bloodline would be Humanoid(Human, Orc) which, by extension, gives them the same subtypes as a half-orc or a Human with Racial Heritage(Orc) so they'd also qualify for Half-Orc rules elements.
So this dose work?
Yes, the bloodline makes you an orc in addition to what you were before
Any rules elements with race as a prerequisite work off the Type/Subtype system. So if it requires you to be a Human, mechanically speaking, it means you need to have, by some means, Humanoid(Human). This could be from being the Core race Human, being an Aasimar with Scion of Humanity, a half-breed race with Humanoid(Human, Whatever), or a custom race that is Humanoid(Human) but modeled differently (similar to how Drow are Humanoid(Elf)). So a Human with Orc bloodline would be Humanoid(Human, Orc) which, by extension, gives them the same subtypes as a half-orc or a Human with Racial Heritage(Orc) so they'd also qualify for Half-Orc rules elements.
I'm not sure about this. Half-Elf and Half-Orc are there own thing, in addition to being able to get the parts of the two halves.
I wouldn't expect a human with racial heritage(elf) to be able to take half-elf feats, archetypes etc. Perhaps I am wrong on this, but I'd like better evidence.
I will note that Drow have their own feats, archetypes etc, and those aren't available to normal elves even though both have the same type and subtype.
A human/orc isn't a half-orc
A human/orc isn't a half-orc
So I am a human and a Orc for feats and stuff?
Yes
A human/orc isn't a half-orcSo I am a human and a Orc for feats and stuff?
You qualify for Human stuff, for Orc stuff, but not for Half-Orc stuff.
By the way, if you are a Half-Elf with the Orc Bloodline and Racial Heritage - Goblin, you count as: A Half-Elf, a Human, an Elf, an Orc, and a Goblin.