Dear Disgruntled Resident,
There are a few things that strike me as unusual about your situation.
First of all, I'm not clear on why you would only get free internet for March and part of April. Google Fiber does offer free internet (at average speeds) after a $30 connection fee, but that plan lasts for 7 years. If your landlord is still charging you a separate fee for internet even though he is taking Google's offer for free internet, that seems wrong to me and you should confront him. That having been said, your landlord could also be installing Google Fiber to provide you with gigabit internet speeds, which does cost money. So find out the facts before you accuse him of anything.
You're correct that your landlord is limited in what he can use your security deposit for. The BYU off-campus housing contract defines those reasons in paragraph 21:
The landlord may apply the security deposit to any of the following obligations of the student:
A. rent owed under the terms of this contract,
B. damage to the property done by the student individually, or by persons invited on the property by the student, beyond reasonable wear and tear,
C. other fees provided for in this Agreement, and
D. cleaning of the unit, unless reasonably cleaned by the student, reasonable wear and tear excepted.
If you chose to take anything to the off campus housing office, the first thing they'll do is ask you if you've made a good-faith effort to work the issue out with your landlord. The off campus housing office expects students to work out issues with your landlord before taking it to BYU. I would speak to him in person about your concerns. Don't be combative, just let him know that you feel he may be in violation of the contract by using your deposit for the improvement he wants to make to the apartments.
If it were me, I wouldn't make a huge deal about the $10. Of course, I am a nerd and would gladly pay a fee to use Google Fiber, so I may have a biased perspective. However, the maintenance issues you brought up seem more serious to me. The BYU housing agreement includes by reference the BYU off-campus housing handbook, which talks about the landlord's obligations to maintain your apartment in section 17 (on page 20). It even lists mandatory response times for very serious problems. For example, paragraph 17.05.09 requires landlords to respond to a "tub and shower or kitchen or bathroom sink(s) with inoperable drain or no hot or cold water" within 12 hours. You may want to try looking through it and see if you find anything.
Above all, make an effort to communicate with your landlord kindly. Explain your issue in a clear, concise, and pleasant way. If that doesn't solve the problem and you feel that your landlord has violated the contract, contact the BYU off-campus housing office.