How much information is too much for a statement of purpose?
I doubt these sorts of statements matter very much.  They are basically fluff and would presumably occupy just a few sentences in your statement of purpose.  However, I'd be inclined to omit both of them, to avoid potentially giving the wrong impression:


  At my core, I think I want a PhD more than anything because I want to deeply challenge myself. Obviously, I have a passion for my field as well, but if someone asked me why I was doing it I'd say it's because of the need to push myself. Is this something to say in a personal statement, or am I better off leaving that out?


The difficulty is that there are many ways to challenge yourself.  You might run a marathon, master a foreign language, or raise lots of money for your favorite charity.  Because of the many ways to satisfy a desire for challenge, this motivation doesn't necessarily lead to stability over time.  Once you have completed your Ph.D., your academic ambitions may be satisfied and you may feel more attracted to a different challenge.  From your advisor's perspective, that would be a suboptimal outcome.  The purpose of a Ph.D. is preparation for a scholarly career, not checking off "get Ph.D." from a list of unrelated challenges.

Wanting to push yourself certainly isn't a bad thing.  If you didn't enjoy a challenge, then getting a Ph.D. would be a bad idea.  However, a desire for challenge is not in itself a very compelling reason to go to grad school, so I'd instead highlight the reasons you chose this particular challenge.


  One school I'm applying is a top 10 school, and it's a bit of a reach for me. Is it a bad idea to say that I've always wanted to get into that school specifically? Will that imply that I'm applying for the wrong reasons? This school is right next to where I grew up, and I've always wanted to study/research there.


This won't help you get admitted: fulfilling your childhood dreams is not one of the admissions committee's goals, nor is it relevant to whether you'd make a good grad student.  It could come across as off putting (for example, if you seem too interested in the university's overall fame), so it would be best omitted.