I'm pretty sure there are a lot of examples that disproves the theory that pureblood is automatically stronger. There have been a lot of really talented Muggleborns and halfbloods in history who have been more powerful. Tom Riddle was a halfblood, and he was way more powerful than your dad could have ever been, or you, for that matter. Granted, Lord Voldemort was a crazy person, but still. Way more powerful. So I think it's short-sighted to say that your lineage automatically makes you more powerful, to put it nicely. Maybe you just haven't bothered to find out how the rest of the world works, outside of your very small, isolated bubble. (Which isn't to say the bubble is your fault, that's your parents' faults, but you're grown up enough now to find out the truth for yourself.) There was an entire world full of magical people out there, people who did incredible, innovative things.
You don't have to figure it all out at once. A lot of people go half their lives thinking they want one thing, and then they realize they're unhappy because they wanted something else all along.
Sure, but it wouldn't be the same. There aren't enough murders for me to solve here, and no one's going to want a zombie for a doctor.