Norm
1. I want to get one outright. Prefer no plans, but if so, what is the
absolute cheapest option available - based on the criteria below.
Not sure about this one - you'll have to research this one yourself.
2. Can I use my existing sim (Telstra 3G) and stick it in (work pays for
my phone bills).
Yes, absolutely. This is what I did and it's seamless. Just import your SIM contents when you fire it up for the first time.
3. I don't really plan to use the internet features (ie, surf the web etc)
I really want it for the apps, listening to music, etc. and as a phone in general. Depending on the apps, I guess some need internet connectivity.
Apps will, if you access the AppStore app, update themselves automatically. Best to do this in a WiFi area and not over 3G. You still have to kick off the update download by selecting those you wish to do at the time - so you're safe from accidental data transfer. Some apps will like to talk to the net in order to download images, etc - or take you to a Wiki reference if you ask it to. Other than that - you can download apps and music and update them from your desktop if you prefer.
4. Are the prices the same in most places or do they vary?
You don't get apps from "places" perse - you get them all from the AppStore. Most app publishers will ask their own price - and depending on the complexity they range from free to over $100 for the navigation-type aps like TomTom and Navigon. Typical price is under $5 though for most apps - and even down to $1.99.
5. 16gig or 32gig - what should I expect to pay?
Not sure - not cheap off-plan though.
6. Wifi - so does that mean I can sit in Maccas and surf the web for free or hook it into my home network?
Yes. Absolutely. I surf all day long on mine via my Wifi home modem. I also call friends overseas via Skype-to-Skype for free. I'm also in IT and support all of my remote servers via SSH and RDP. Brilliant! 
7. I really just want the astronomy apps - do they need internet connection to work.
Again - some do to go and get info that you've asked for. Mostly though - no. They work independently in the field.