Sounds like someone did not get a qualified home inspection?
I agree, those lines coming in look larger than 60 amp.
Just can never tell from the pictures. Sometimes I wish I had the Enterprise so I could say, beam me over there Scotty!
The service entrance cables are ok if they are AL. Thats how most places are. These are a larger guage wire with grease at the lugs. Dont ever remember seeing copper entrance cables.
Just call an electrician or 3 and get more advice and price.