Can I deduct my annual credit card fees which are used almost exclusively for my work (non-reimbursed). I.e AmEx fee which is used due to rental car insurance coverage.

For a work credit card, fees that are incurred are deductible.  The question would be "did I get this credit card because of my business and do I use it for my business with little personal (or none for the IRS) use."  Per the IRS: To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your trade or business. A necessary expense is one that is helpful and appropriate for your trade or business. This link has  some more Information.

Business expenses

Does this same thing apply if I am an employee? In my case a professor who travels weekly. The credit cards are both "personal," meaning not a business card per se, but the entire reason that I have them is due to the business perks; meaning, that the AmEx is due to the rental car insurance coverage.

As an employee as long as necessary and are not  reimbursed These expenses are miscellaneous itemized deductions on schedule A.  These expenses must total more than 2% of your AGI  to start counting as deductible.