Municipal water systems have a "sanitary sewer" line in addition to a stormwater line. I've no idea how this method of virus testing works, but I beleive you would take samples from the sanitary sewer.
That depends on system design. Older systems tend to be combined systems, unless they've been reworked to separate stormwater. If you live in or near somewhere that often has sewage outflows in heavy rains, chances are it's a city that urbanized before WW2 and has combined sewers.
Sanitary sewers also tend to be leaky, rain will result in surface water entering the sanitary sewers and larger flows into the treatment plants even if storm drains are routed elsewhere. You might get some filtration from soil though. If your city only very occasionally has sewage outflows in heavy rains, it's probably from ground inflows rather than combined sewers and there may also need to be a second trigger such as power loss.
Back to the original topic, I think the above is interesting but irrelevant. If your system is at risk of bringing in stormwater to screw up your measurement, you'd change where you're taking the measurement and/or be a little selective about when you take the measurement.
Lots of stormwater lines in Texas cities/suburbs are straight to water sources. Lots of PSAs and signs and what not about storm drains going to rivers and lakes and what not. They don't often hit a lot of treatment plants.
As a kid I had a lot of fun exploring the underground of the storm drains.
I'm assuming that would be somewhat unusual, I doubt that any of the water that gets in contact with farm animals is supposed to drain into the municipal water system.