Unless that basement becomes a swimming pool (rather than just a little seepage during downpours), I doubt you're obligated to remedy that.As for mold because of the clothes pile near the moisture....is it not really just mildew?

I'm looking at a building where the disclosure has an EPA report for remedial action completed 20+ years ago due to a radiation superfund site that was found nearby in the 1960s.  

I also had a flood.....NEVER do water remediation. 

Yes, the few thousand may sound like a lot today, but once you step in the chain of ownership, you can't undo it and can be liable for remediation. 

But Realistically My biggest concern is having to Get / Pay a EPA compliance company to come in and tell me everything is OK or wether some type of Remedial work needs to be done to be in compliance before the project even begins . 

In exchange for this permission, the Tenant agrees as follows:1.To keep no more than 1 domestic dog(s) as described below.2.To pay additional rent in the amount of $ 0 per month; or3.To deposit with the Landlord a "Non-refundable Pet Deposit" in the amount of $ 250 which shall be held as security for the faithful performance of this pet Agreement and shall be used upon the termination or expiration of this Agreement for the purposes of cleaning the Premises.4.To keep the pet from causing any annoyance or discomfort to others and to immediately remedy any complaints concerning the pet.5.To keep the pet from damaging any property belonging to the Landlord or others.6.To immediately pay for any injury, damage, loss, or expense caused by the pet (In this regard, it is expressly understood that at no time shall the Tenant apply any part of the Pet Deposit towards such amounts due, but rather, the Tenant shall make restitution immediately and separately from the Pet Deposit.7.To keep the pet under control at all times.8.To keep the pet restrained, but not tethered, when it is outside of the Premises.9.Not to leave the pet unattended for any unreasonable periods.10.To hold the Landlord harmless from all liability arising from the Tenant's ownership or keeping of the pet, including but not limited to any liability resulting from the Landlord turning said pet over to local pet policing authorities should the pet be found unsupervised.11.To dispose of the pet's droppings properly and quickly.Also, to coordinate the cleanup of the pet’s droppings with the weekly lawn maintenance.12.To insure that the pet will wear the appropriate Local Animal License, a valid Rabies Tag and tag bearing the owners name and phone number.All licenses and tags must be kept current.13.Tenant agrees to control flea infestation and will exterminate if necessary, and upon demand, in any and all areas affected with full cost to be paid by tenant. 14.Tenant agrees that Landlord will not be responsible for the injury, harm, or death of the animal, and agrees to hold Landlord harmless for any damages suffered as a result of any harm caused on the animal or by the animal upon another person, guest or employee.

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You have to remediate it and disclose it from that point forward.  

Best options are to get an asbestos remediator (read: expensive) or to cover the floor as is. 

Remember that FHA mortgages have very stringent requirements for condition of the property, and its possible the current owner has gone through the inspection process and found that the property is lacking in certain areas, perhaps in items that the owner is unwilling to remedy prior to sale.Last note: you wrote that the owner specified it would NOT be able to be an owner-occupied purchase... was the property fully rented with leases in place?