One other thing to mention about the reg being right close to the heater. It could be that you have a 2lb gas system at your house, and this reg steps that 2# down to the low pressure the heater wants. This setup allows for smaller gas pipes between your meter and the heater. If this is the case, you likely have another reg between your meter and your house to step the house down as well.
And yes, vent points down. Some can be piped to another location, some can't.
And yes, vent points down. Some can be piped to another location, some can't.