If something were to happen and the insurance adjuster sees the house was being rehabbed your claim can be denied.If your policy lapses that are not good as a lender-placed policy is to protect their interest thus you are still on the hook for liability and your content.

Property has 3units 7bd 3ba Sqft 2352 build 1962 Style CCCustomer is willing to hold the note on the home with set amount she is older and don't count on living forever.2 units occupied total of 2870 in cash flow1st flr $1790mth  3bd 1 ba2nd flr vacant ($1700-$2000 potential) 3bd 1baStudio $1080mth 1bd 1baTaxes is $12321.27yroil 3 zone furnace City Water 2 Electric boxesLocated 45 Min from New York5 min from University and College3 Different Mountain Trials and Parks  Shopping District and Medical Centers What questions would you ask?

Could they claim that they're entitled to reimbursement immediately and in full from me? 

I've filed a insurance claim and have sent my tenants texts, emails and certified letter that the house is potentially unsafe and they need to vacate the property until I can get repairs done.

You would certainly want protection for yourself if you are hurt and out of pocket for a number of weeks or months, but not sure what options you have outside of the standard health/medical insurance for yourself.  

However, the tenant is now claiming his actual rent was $2800, and that he did not sign the lease that we have on hand.

They can claim that the stable, non-gentrifying city has equity....as it falls into decay.   

Can the sub-tenant claim that they will stay and the primary tenant must keep paying as per the agreement?

Your income is $1600 AFTER expenses, so you can't then claim those expenses again. 

She reported mold in the basement, claiming that she got sick from it but provided no evidence, no diagnosis from the doctor, and no mold test.