I like the guy, but ...dang.We gave him a sweet deal since he would have to be more concerned with the tenant below as there is no separate utility for the basement, he would have to be mindful of noise and place the basement tenants' mail in his mailbox out back. 

I’ve been dealing with various complaints (on a fouplex) from the tenant in first floor about upstairs tenant making too much noise, he says that basically all day and even at night they are getting too much noise.

Meaning... we seperated ourselves from the noise.

Example problems:Applicant deniedApplicant approved, fails to pay depositApplicant approved, fails to move in or pay rent on scheduled dateTenant moves in, complains about condition of rentalTenant adds unauthorized pet or personTenant pays rent or other outstanding charge lateTenant doesn't pay rent or other outstanding chargeNoise complaint or other lease violationMultiple noise complaints or other lease violationsTenant abandons rentalTenant moves out but leaves property behindTenant wants to terminate early for personal reasonsTenant wants to terminate for loss of job, death, or other legitimate causeYou want Tenant out because they're a pain in your neckTenant refuses to allow you access to inspect or conduct maintenanceYou can read BP and get a list of the most common issues.

Is it reasonable to assume that a cease and desist order is related to noise or some sort of public disturbance rather than a violation of a code that does not exist?

Just reading your post has inspired me to be patient and grind it out as my first acquisition is taking months to close.

gluing hardwoods down is the best option and controls noise, movement, water penetration far better then nail and floating options. the trade off is it takes 3x longer to install. so it really just matters what you goal is and what your willing to do or spend to get there.

The grind worked great as we had it all to ourselves.

Yes, trusting random people outside can be scary and that's why it will be a grind at the beginning. 

Way to block out the noise and take the steps necessary to live out your dream.