Corporate iPhone but on personal wifi. What can the employer see? Can they see the browser history and website

Fire. Unfortunately that would seem to be at odds with Amazon's return policy.

If Disk Utility can't see the drive, it's unlikely you'll be able to access it to overwrite anything (and overwriting on SSDs can be tricky in any event). Additionally, because the drive in the rMBP is a proprietary form factor, it's difficult to take it out and try to access it from another computer (which might not help any way). There may be adapters made in the future, but I'm not aware of any for sale at the moment.

The best preventative measure for this would be to employ some form of whole drive encryption, like Apple's FileVault. That way even if someone is able to read the data off the drive, it won't be useable unless they have your encryption password.

On iOS, HTML5's local storage is not available in private browsing mode, which means you can detect it by attempting to save something to local storage and catching the exception with the following JavaScript:

try { localStorage.test = 2; } catch (e) {
  alert('You are in Private Browsing mode');
}

^{Modified from https://stackoverflow.com/a/17741714/}

On OS X, there's not really a canonical method, but this should provide some useful information:

• Can web sites detect whether you are using private browsing mode? –Security.SE

If you're looking for implementation guidance, you should probably try Stack Overflow instead