Can I use domain names that are similar to major brands?

Generally, you cannot register domain names that include a trademark of a third party, if use of the mark in the domain name is designed to take advantage of the goodwill embodied in the mark reflected in the URL. The word or phrase used in the URL doesn't have to be registered as a trademark per se, as Simon pointed out.

What you have described appears to be a situation where you would be infringing on a third party's trademark rights. Unless the website you are building has some sort of non-commercial aim (i.e. used solely for informational purposes without any intent to profit) or if you can otherwise prove that the use of your domain does not infringe on the third party's trademark rights (i.e. because you were using the mark first or you are using the mark on goods/services that have nothing to do with the trademark owner), you are in hot water with the trademark owner.

I suggest contacting an I.P. attorney on this matter.