When edting permission level at Sharepoint the Design level has the 'approval' option with the 'edit site' enabled. By default when I click at approval option, it automatic checks the edit box, even if I try to create another permission level. Is there any option for just allow approving?
Permission Level Approve includes Edit and approve pages, list items, and documents for publishing sites only.
Contribute permissions, plus Approve Items
So you can't restrict approvers from editing a list item. http://technet.microsoft.com/en-us/library/cc721640%28v=office.15%29.aspx
Not OOB. Approving an item changes values within the item, and so therefore approvers need edit access. It would be possible for a developer to build a SharePoint solution or app that could run with elevated privileges and approve items.