On the corrupted Data, Yes, restoring and reformatting will fix the issue, that is what the options are there for, but keep in mind, if the corrupted file is large, it is likely to cause you a lot of lagg on the PS XMB.
On the internet problem, I suggest going to the PSN website and entering those in the error diagnose section. Each error has it's own specific code, as you would have thought, and some of them are part of groups.
80710102 - Issue connecting online
The system is unable to connect to the Internet. This may be caused by inputting the incorrect information when setting up your network connection, or it may be a temporary fault with your connection. For example, if using a Wireless connection, this could be due to a weak signal or, if using a wired connection, due to congestion with your Internet service.
I can't get you details on the other error because the error section of the site is down for maintenance. But from what I have read, scouring the internet through the trolls and illiterate people out there, I have gathered enough information to suggest that possibly the network is having some downtime for your region?
I suggest waiting a few hours, and power cycling your modem (Turn it off from the switch or router for 15 seconds then turn it back on)