I'm sorry if this is the wrong thread but what do these mean and do thay effect anything?

Inbred means breeding Sylesti that are related to each other. The more you do this, the more the Inbred Percent an offspring will have. Purebred (in this case) means NOT breeding related Sylesti. No, they don't affect anything other than a number on the pages of a Pet's Lineage.

I see. But I heard pets that are siblings or hafe siblings will not breed with each other. So how far apart do thay have to be to breed and as a family tree gets bigger and has more branches will there be a point where there too far apart to be considered related, I doubt this because I don't think sylestia is that advanced in pet genetics. But it would be interesting to know how advanced it is. ;)

Actually, yes, there is a point where two distantly related Sylestis will not count as inbred.

What I know of the limits of inbreeding is that yes, siblings and half-siblings will not breed. Neither will son-mother or daughter-father pairs. However, a sibling of the parent can breed with the offspring of said parent. (uncle-niece/aunt-nephew relationships)
I hope this information helps you. :)

Thank you I was wondering what it was. I think it's really cool that this game has so many possibilities in breeding. It's so nice what you can make with the generator aswell.
Thank you for answering my questions. Have a nice day!