1. I'm confident in saying that there is no way (yet) to suppress tweets.
2. What tweets are displayed is based on
a) the tweet must be geocoded (tweets have the option of including a location), AND
b) the tweet uses some keyword
So if I send a tweet that is geocoded with words like "detour", or "traffic" or "accident" it will appear on the screen of Wazers in the area of the geo-location. It works like a chit-chat, so it doesn't pop up unless I am stationary.
Waze will also include all tweets from a tweeting source of traffic info, but pretty much only if they are geocoded or can be tied to a very small road segment.