Is someone trying to hack into my computer via the app store?

Just changing your password should be sufficient.

Best to do that on a timely basis. At least once a week.

For your email. Try a reset ...

Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.

If that doesn't help, tap Settings > General > Reset > Reset All Settings

No data is lost due to a reset.

Is it possible for someone to hack into my computer using my Apple details as a way in? Not saying its not possible but that's why changing the password often can prevent that from happening.

I suggest you call Apple.

Someone had a similar problem. Please read this.

https://discussions.apple.com/thread/5118974?answerId=22300883022#22300883022&ac_cid=ha123456#22300883

Hope this helps.

apple doesnt get "hacked", but if you have concerns see this

http://support.apple.com/kb/HT4232

peace, Clyde

I just saw this recently posted question. An Apple community specialist answered it. Please note the site the specialist is telling him to go to. http://appleid.apple.com

The discussion the poster in the previous reply I sent you got her email from

appleid@id.apple.com

This seems like phishing. Change your password again.

I suggest you call Apple to discuss it with them as soon as possible.

apple doesnt get "hacked"

Nonsense! Apple IDs get hacked all the time.

Apple alerted me that my ID and password have been hacked into by someone in the US downloading a free app - which arrived on my i-pad.

That certainly sounds like the symptoms of a hacked Apple ID. Note that you should not click on any of the links in the e-mail you received. Instead, go straight here:

http://appleid.apple.com

Change your password, making sure to select a strong one that cannot be guessed. Then, I'd strongly encourage you to turn on two-factor authentication to prevent people from taking total control of your Apple ID:

Apple introduces two-factor authentication

should I change my Apple ID as well.

Changing your Apple ID would mean losing all purchases you have made with your current Apple ID. That's not a solution to this problem, and will cause you other headaches.

Since then - all my emails indicate the time as an hour behind the actual time - is this related - or just a mal-functioning coincidence?

Coincidence, most likely. I can't see any reasonable way for these things to be related.

Is it possible for someone to hack into my computer using my Apple details as a way in?

If someone gets access to your iCloud account (which, for most people, is their Apple ID), they certainly may be able to hack your computer in a variety of ways. If you have turned on Back to My Mac, they can get access to your computer that way through your iCloud account. If you have turned on Find My Mac, they can locate, lock or even remotely erase your computer using your iCloud account. Both of these would be enabled - and can be disabled - in System Preferences -> iCloud.