1) Why is a S5 (or S3 - but there was no S3 so I'd have to purchase online) better than a Sony Cyber-shot DSC-H9? They seem pretty similar in size and features, although the Soney goes up to ISO 3200 (not that I'd ever necessarily want or need to use that) and has the 15x zoom.
There are several reasons why the S3/S5 is better (IMO) than the Sony H9:
The S3/S5 has a lighter approach to noise reduction ... though the pictures might look a little grainier, the S3/S5 retains more detail that can be extracted with better noise reduction software. The H9 is more heavy handed with it's in-camera NR and tends to blur detail at the higher ISOs (not that you'd ever want to use them!).
The S5 has a flash hot-shoe for attaching an external flash.
Both S3/S5 have a folding/flipping/rotating LCD which is great for composing unusual shots like very low to the ground or high above your head.
The S3/S5 have the best video available in a digicam.
The S3/S5 have faster lenses (3.5 at full tele vs 4.5.
2) The salesman really pitched to me that the Sony would be better given the lithium ion battery that can be recharged as opposed to needing to change out the AAs after 125 pictures or so. He didn't tell me the cost of the battery, which I've read to be about $60. Is relying on the AAs going really to be such a big hassle time- and -expense-wise?
Nickel Metal Hydride (NiMH) AA batteries are cheap and reliable ($5 - $10 for set of 4 w/charger at most electronics stores).
I get well over 300-400 pictures (with LCD and occasional flash) from a single set of 2500mAh batteries, and shot all day long at Disney with just two sets of batteries.
Plus, in a pinch, you can always buy AA batteries just about anywhere. If your proprietary Sony battery dies in the middle of the day on vacation, you're out of luck. With AA's, you can just go buy some from a gift shop.
3) I keep reading "SD" here - what does that mean?
SD is Secure Digital ... it's the type of card that the S3/S5 camera uses. SD memory is cheaper and more readily available than Sony's MemoryStick. And, now with SDHC, you'll be able to get SDHC cards with 32G capacities!
4) Will a 1 GB memory suffice? What does the camera come with upon purchase? If I'm uploading my pictures to my laptop daily, will I need something bigger than that?
It depends on how many pictures you expect to take and how much video you're likely to shoot. Video chews up memory cards very fast (~8min/G!).
When we went to Disney, we took 7G worth of SD cards (3 2Gs and 1 1G). There were a couple of days were I needed all of them!
5) The S5 won't work in extreme cold - how extreme is extreme? Will it survive in cold Ohio winters, or chilly Florida nights?
I've never heard that S3s/S5s "won't work" in the cold ... I took dozens of pictures of an ice storm a few weeks ago with no problems.
The *batteries* can have problems in the cold, and you shouldn't charge them where it's very cold (below freezing). But, the camera itself has no problem with cold that I'm aware of. It also helps to keep an extra set of batteries warmed in your pocket when shooting in the cold.
You'll have no problems in Florida.