I see two problems with my lawn:

1) There are dead patches scattered about. I'm thinking this might be dog urine burn, since I have a female Labrador who spends a lot of time outside. I have picture below, please confirm if this is dog urine burn.

2) Some type of moss is taking over my backyard. I have a stream (not a clean one) flowing through the back of my backyard, and it occasionally floods onto the further half of the lawn. The moss is more prevalent in the grass closer to the river. However it's becoming a problem closer to my house as well.

Any help/advice is greatly appreciated!

Back of lawn closer to river

Front of lawn closer to house