Am I at fault? Can I get my security deposit back from Landlord?
The landlord is wrong, and he should reimburse you the totality of the security deposit.
Clauses #1 and #16 would entitle the landlord to deduct from your security deposit only the portion of the 7-day period that is not already covered in the payment you made for 1st week's rent, which according to clause #1 starts on Sunday July 29.
If I understand correctly, you signed the contract (and paid) on July 27, and then gave your 7-day notice on July 28. Since you paid an additional amount for Saturday July 28, then your 1st week's rent payment actually covers the entire 7-day period of your notice. Therefore, the landlord should reimburse you the entire security deposit.
The contract nowhere indicates that the count of [post-notice] 7 days starts after the current rent-week elapses. But even if it did contain language in that sense, the dates you mention render that hypothetical clause void.
Lastly, clause #16 refers to giving a written notice, which is what you did by sending him the text he obviously read and understood. Therefore, his statement that "you did not provide proper notice of moving out" clearly is false.
What should I do?
If the landlord insists to retain the security deposit, your option is to file a complaint in Small Claims court (I don't know whether this has a different name in PA). Depending on PA procedural law, you and the landlord might be cited for mediation prior to being assigned a court date.
A process in small claims court is pretty straight-forward, but only you can determine whether the hassle of attending mediation and court hearing is worth. If anything, it (1) certainly gives you some [minimal] exposure to litigation, and (2) teaches the landlord to abide by the very rules he drafted in the contract.