What can a wifi administrator see? Can they see all of my search histories?

As you are wondering what can a wifi administrator see, you should know that someone who has administrative access to the network you are connecting to can: View the IP address and domain names of the site you're connecting to (based on DNS query and/or SNI in TLS) and which email provider you're using, irrespective of encryption. You can prevent this by using encrypted third party DNS (e.g. DNSCurve to OpenDNS).

The location of your access point (this is of little concern for you as you're physically neighbors anyway). View and modify the content of any unencrypted traffic, including session keys/cookies, and passwords if they're traveling over unencrypted connection. View and modify emails traveling over unencrypted POP, IMAP, SMTP, or unencrypted web mail. Block access to any site or protocol, irrespective of encryption. This may in many cases be circumvented with a VPN/proxy. In extreme cases, the administrator may block all proxies, VPN, and Tor. View and modify encrypted Wi-Fi packets and its content, that is not further encrypted (e.g. with TLS)

They can't: View and/or modify content, session keys/cookies, or password traveling inside end-to-end or user-to-service encryption (e.g. PGP, TLS). Snooping into these type of encryption can only be done if your neighbor installed a malware/certificate in your computer View or modify the content of emails or who you are sending email to when using POPS, IMAPS, SMTPS, or encrypted web mail. Doing these kinds of interceptions do require a little tech saviness, but it's not actually that difficult if they really wanted to learn how to snoop on you. Also note that there are a number of other non privacy risks with sharing connection with others. For example, if your neighbor accessed illegal activity, they could potentially implicate that on you and you could be dragged into these legal problems.