I'm suspicious because the Binghamton area is a good rental market, but it's not usually that good.

Give them your business card with phone number and tell them that if you see anything suspicious call the police and you no matter how late or early.Gray area stuff, the home isn't yours and you could be in hot water if the listing agent or seller find out that you placed a cage over the unit before you close so tread very lightly.   

Situations will vary but I would be suspicious if there was any pushback from seller when requesting these documents.

The idea makes sense, but I'm still suspicious. 

We didn’t find anything suspicious at the moment because everything seemed to be OK with the credit cards.

Though if it was me, I would open checking account with other bank or let the current bank unfroze my account so I am with you, I feel bit suspicious. 

Nearly anything else is suspicious. 

If you purchase under an entity it looks extremely suspicious.

Living in a hotel is a red flag too, unless their last house had a non-suspicious fire.I had a single mom look at a house once and her brat was into everything.

Plus, making out in a half finished rehab is fun as long as you brush away the tell tale signs of suspiciously placed drywall dust afterwards.