iTunes and Apps app error

So I've bought the new iPhone 5 recently, however I've come across two errors (which might be relative to each other)

#1. My apps store used to work, and I was able to download a few free apps, but now the Apps' search engine won't load. When this happened I noticed that my iTunes wasn't working as well.
Trouble shooting steps taken:
- turn phone off/on
- double clicking home button and closed down app and reopened
- settings>general>reset>reset network settings
- settings>general>reset>reset all settings
- sync with iTunes on my laptop

#2. Now, when I tried to sync with my iTunes on my laptop, I was prompted to update my iTunes to 10.7 or later. So I did downloaded the most recent iTunes on the Apple Store. However, my laptop needed a software update. Tried doing so, however there is no software update available for me to do on my laptop. Apple>System Preferences>Software Update

Assistance would be much appreciated

I think what you are trying to say is that you are trying to sync a brand new iPhone with a very old Mac.

That's not going to work out very well.

Possibly what you mean is that your Mac isn't THAT old, but you need to jump up to a PAID upgrade (like to 10.6 from 10.5) in order to get iTunes 7 which will in turn work with the iPhone 5.

Bottom line: if your Mac is running 10.5, it's really kind of old and while you will probably get around the issue this time, this sort of thing is going to keep happening if you keep on buying new toys and trying to attach them to old equipment. Just so you know.

So, what to do: if you're on 10.5, you'll need to buy a copy of 10.6 by calling Apple on the phone and ordering a DVD ($30+shipping). Once 10.6 is installed, do all the updates to get 10.6.8 and the Mac App Store. Then your iPhone 5 and iTunes 10.7 should work.

Then we'll need to know more in order to advise you further.

The free alternative would be not to use your iPhone with iTunes. It's now possible to do many (not all) things without ever connecting your phone to iTunes