Is it safe to run Tor from your home computer without a hardware firewall? I'm assuming having a firewall isn't a major requisite, since people are using Tails on public wi-fi networks, but just checking.
Also, is there any correlation between the way you connect to the internet (dial-up, DSL, T1, etc) and security? Actually, I think Tails doesn't even support Dial-up, but you get the point. Does Tails support pppoeconfig?
Yup
The software firewall in Tails is brutally harsh. Only allowing Tor & I2P traffic to see out (normally - I'm ignoring the "unsafe" browser shenanigans for simplicity). It almost certainly affords better protection than a hardware device would!.. unless you'd spent considerable effort setting it up just like Tails'! :D
Might be worth thinking about NAT, etc if your connection is indirect... but nothing significant springs to mind.
Sadly not
Can't help at all there. Never tried, never looked.
See ?Add Gnome PPP for Dial-Up Users for more information on tentative dial-up support. To sum it up: it's unlikely that it will work if NetworkManager does not get support for old style serial modem.
Mobile broadband works fine and DSL or other PPPoE connections should work fine as well. All of them can be configured through System → Preferences → Network Connections.