Why are these ports open on my iPhone?

The squid proxy, on port 3128, is used for WiFi hotspot and wireless data tethering.

The iphone-sync port, 62078, is to enable iTunes to wirelessly sync via WiFi[0] with your iPhone.

I believe port 80 and 8080 are opened as service ports. When under service, Apple repair technicians can sideload service menu apps onto the phone and browse to the phone's IP in a browser to get various debug statistics and perform other maintenance actions from the phone. Also remember iPhones are built on Darwin on ARM so those ports could just be opened by default to allow Apple services to connect to them (e.g. Find my iPhone, iCloud, APN, etc.).

[0]: http://support.apple.com/kb/HT1386