You would need permission from the landlord in order to do this and most are not going to be ok with having an "unknown" tenant in the property especially if they don't know you very well as a tenant yet. 

And how do you word your addendum for permission to rent it to short term guests?

Also they sign for permission to verify the info on the application.  

Something like " the below grade area has its own entrance and is finished as a third unit with four rooms and is reportedly rented as a separate unit" it is beyond the scope of this analysis to determine if this is a legally permissible separate unit however county assessment records do not mention it, so I have assumed that it is not legal and given no contributory value" or with the ending " If found to be legal, the space would contribute $xx,xxx to the subjects market value." 

sounds like a private note thoughU can do subject too and dont ask permission and if the mortgage and note has an alienation of title clause the lender at their sole discretion can call the note due.. so be prepared to pay it off if that happens.Or you can wrap the note with an all inclusive Deed of trust if those exist in that state.

Typically this is a permission form you would have them sign as an addendum with the lease, where they give you permission to draft their account the first of every month. 

If the tenant hasn't given permission and you haven't provided the notice required notice according to the lease I wouldn't allow access.

Tell her she is not allowed to move additional people into the unit without your permission and that they must pass your screening process and, if approved, sign the lease. if she refuses, evict.

Buying a property with a hard money lender is always permissible. 

If it were me, I would deny the animals and give them a stern warning about adding animals without previous written permission.