All the pool equipment is there but needs to be ran again to get back working.

You might also consider any furniture or equipment of value either as collateral or to be given as part of the compensation.

I hired them because they project manager who oversaw the rehab at the properties was not equipped or experienced in property management. 

Is it OK that the equipment and pump shed is unsightly?

He is on site and has the equipment.  

I'm not sure if this applies to ESAs (though I do know that it is not legal to deny tenancy to someone with an ESA), however, when it comes to service dogs (ONLY dogs and the odd miniature horse, can be service animals), handlers are not required to disclose that they have a service dog to a landlord, as service dogs are NOT pets - they are defined as medical equipment under law.

Did the new tenant assume the equipment in the yard was included for their use when they agreed to rent?

PM's are generally great with maintenance however not the most equipped to get you the best price on a large project etc.

Most realtors are better equipped to deal with regular folks seeking a home than investors seeking a deal.

However, you can equip yourself to answer those questions.