First the move out day - generally 1 year leases go from the first day of a month to the last day of a month, so if yours started Aug 1 2012, you must be out by midnight on 7 31 2013. If he is saying Monday, that's Aug 5, so consider yourselves lucky, unless your lease started on the 6th last year. Which would be unusual.
Second, a copy of the lease: you should have not even moved in without a copy of the lease. You shouldn't even go 24 hours after paying any money without it. You hand over the money with one hand and take a copy with the other. He might be lying about shredding but there's nothing you can do now. Without a copy of the lease you are a tenant at will.
As for damages, you need to register complaints in writing, and you need promises such as for painting in writing, and you do need to pay for the damage to the downstairs ceiling when your water line to the fridge leaked. $300 doesn't sound like too much to me for any water damage. But if you are expected to pay it (or it's coming out of a deposit), you can demand a copy of the receipt for the work and materials. If you are expecting $300 because you painted and have nothing about that agreement in writing or receipts, you are out of luck.
'Crazy charges' aren't much help if you are just speculating so please try to be more specific. If you overstay even one day, you can be charged with a whole month, unless there are people moving in - then you only owe for days that don't overlap.
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