Obviously the 3G won't touch your 20MB speeds. However, using Wi-Fi you could fully take advantage of the 20MB speeds on your iPhone while at home assuming you have a wireless router. I'm guessing 3G is similar to being on 512KB or 1MB connection.
1. Pretty much all newspapers have all news online now. The iPhone is very good with news sites due to the way that most are laid out. There are a few apps which let you browse news, although I have yet to find one that suits my needs. You could also use RSS feeds letting you view the headlines and then just tapping on it to view the full article if it interests you.
2. You could probably check your work email through Safari, although as someone else has mentioned, if you use Exchange it is probably best asking your IT department as they will be able to set it up in the native mail app which is a lot better. This should also push all contacts and calendars down to your phone as well.
3. You can download podcasts using iTunes and then sync to your iPhone. With the latest firmware (2.2) you can download new podcasts direct from the iPhone, either by going to existing podcasts and going to get more episodes, or searching for them on the iTunes Store from the iPhone which can now be done over a 3G connection.
4. It will download even without a Wi-Fi connection, all you need is a signal, it will be slow if you are only on EDGE or GPRS.
5. Yes the internet is unlimited. Fair usage does apply but there is no cap. Apparently O2 will write to you if they believe you are using it excessively.