Hi there,
Firstly, there are ATMs, I have only every stayed in Laganas, however they can run out of cash so I have heard. There are Banks in Zakynthos Town, so I assume there would be more there. But I wouldn't rely on using ATMs as your only source of cash.
It is still really warm in September, although it can get quite cool at night time so I would take something to coverup with. I actually got a realy great tan in Setember (better than July/August) because it was more bareable.
There is a waterpark on Zante, although I have never been so can't comment.
Theres also a trip to neighbouring Kefelonia.
I have been on the trip to Olympia and that was amazing I have to say. But a long tiring day. We did that at the beginning of August and the sun was belting hot so was quite tiring, it was also the year before the Olympics (2003) so many of the museums were closed.
The trip to Smugglers Cover, in my opinion, is a must if visiting Zante. You get to stop off at certain locations to swim (weather permitting) and you also stop at Smugglers Cove and can have a swim, it's amazing.
Night life is Laganas is great, although I am not sure if you are after that. I have heard its good in Tsilivi, but not 18-30 like Laganas is. Laganas does have quite a few quietier bars perfect for families and couples, mostly on the Kalimaki Road, so don't be put off if its not nightlife that you are going for.
If you end up in Laganas, the beaches can be quite dirty near to the main strip, so I would recommend going a little bit further down where it is quieter, towards Kalimaki beach, where it is much cleaner and quieter.
Hope this helps, any more questions then just ask!
Kate