While it's a public street and anyone can park a legally-registered vehicle EVEN in front of your house, kiling grass and creating a muddy mess isn't cool especially since that green space is your responsibility. I suggest talking to them first, simply explain that you wanted to keep the grass green and growing and avoiding bald, muddy spot.
Regarding parking and partially blocking the driveway, it is a parking violation. A vehicle cannot be parked within a 3-foot space from any driveway EVEN IF it's your own. I hate to do the following, but if talking has gotten you nowhere, call and report the violation and the description of the vehicle to the police. Personally, I'm cool with a vehicle parked up to my driveway, even a couple of feet of blockade especially if it's a neighbor I'm on good terms with and it's not a daily occurrence. I myself use that 10'-11' space from time to time and I make sure my vehicle blocking my driveway instead of theirs.