Can I purchase from other sites using my Apple ID? Is it possible to purchase from other sites using my Apple ID account like paypal; to pay for items on sites other than the iTunes store?

How would this be done technically? I have came up with a few possible solutions but doubt them. Would Apple even allow this?
Short answer is: no. iTunes accounts are meant for purchasing products from Apple, and Apple only.

Apple might decide at some point to partner with other companies to allow you to reuse your account on other websites, but I don't think it has done so so far. Besides, iTunes is an online store, not a payment service like Paypal.