Contacts search fails

When I got my iPhone 5 last week, Sprint hooked it up to a little machine and transferred my contacts from my old (Android) phone. I also set it up to sync with my computer, which is syncing with google. So I'm aware that my contacts list is a horrible mess of everyone I've ever emailed, with duplicates, but I've never cared in the past because I've just searched for the name I wanted and it has popped up. It works on my macbook, it works in gmail, it worked on my old phone, etc. (Every now and then I feel like I should clean up that list, but if you had a magic closet that was indefinitely large and would hand you any item you asked for, would you ever bother to clean it? I just don't have that kind of free time.)

But now, when I search for contacts on iPhone, they don't come up, even when they are clearly there. For instance I have a contact called "Physical Therapy". If I type "physical" in the search field on my iPhone, it does NOT give me that result (it gives me a few other random people whose names start with P but don't actually include physical in their name). If I scroll down to P, the contact IS there. So I don't understand why it won't return that result when I search. Its making it very difficult to make calls with my new phone. Since the searching does work for the same contacts on my macbook, I don't think its something silly like spelling or formatting mistakes.

Any ideas what I can do about this? For instance, is there an automatic way to make a list of all contacts that include phone numbers, so at least I could scroll through them more easily if search won't work?

Less importantly, is there a way to link my phone contacts with my facebook contacts so that someone's facebook picture shows when they call me? This worked automatically on my HTC Hero by "linking" the contacts but it hasn't carried over, which is understandable. I did turn on facebook contact syncing in the settings, but it doesn't seem to have an option to match up names that are the same and at least give me the option to link the photos to the phone numbers. On the other hand, pictures don't show up at all when texting and very few people actually call me instead of texting these days, so its not a big deal.

Thanks!