Hi @belz2000
First, you have a number of things going on here and it's probably best you break it out into smaller more manageable pieces.
1 - If you have a new theme and don't require anything from the older provider, then I recommend creating a new hosting profile, installing that theme and starting from scratch.
2 - If you plan to use the old work, or pieces of it, the only sure way of getting it taken care of is engaging someone to provide you a malware review of the site or employing a dev to break out the features you want.
3 - As for your other website, yup, it's infected just see here: http://sitecheck.sucuri.net/results/www.littlebusinesses.co.uk/. You have what is known as a malicious redirect. The complexity in these attacks can range in complexity. A good place to start here is as follows:
- Check .htaccess
- Check root index.php
- Check index / footer / header / functions PHP files in your wp-content
This won't address every case, but it'll likely point you in the right direction. Another great free forum is Badware Busters
Hope this helps. Your other option is always to employ professionals to give you a hand.
All the best
Tony