1. Depends really. If it's a generic home based machine, probably marginally more than simply having it connected to the net. If it's based in the pentagon with a machine name like "National Secrets storage device" then probably more of a risk.
2. Make sure your firewall is configured correctly (i.e. only open/forward the port(s) your dominions server is using). If possible, run from an account with limited priveleges (and make sure the admin/root account is password protected). Make sure your antivirus is up to date too.
To be honest, the risk of being hacked is fairly slim, unless your clearly connected to a corporate organisation or similar. The biggest threat is being infected by a worm or similar virus, which a decent AV should be able to take care of. Then again, depending on the machine manufacturer, the biggest risk may well be hardware failure
