The first picture looks like a weed which could be treated with Weed-b-Gon.

Second picture looks like nutsedge but it looks like it is diseased. Nutsedge thrives in swamps and in lawns which get far too much water. When the lawn is allowed to dry out for a week between watering, it will go dormant until it rains or you start over watering again. You should be deep watering, once a week in the hottest heat of summer. That is a guide. Some people have to water an inch every 5 or 6 days, but you should never water every day or two. Deep watering means 1 inch all at one time. Put some tuna or cat food cans around the yard and turn on the sprinklers. Time how long it takes to fill all the cans. That will be your watering time. Mine is 8 hours for my hose/sprinkler/water pressure combination. Your time will be different.

The 3rd and 4th pictures are pictures of urine spots from dogs. Treat those by dropping a heaping handful of table sugar onto the spots. The sugar stimulates the microbes which usually decompose urine to go into repopulation mode. In 3 weeks the microbes should be in place and the spots should be gone. In order to keep this from happening in the future, start making organic fertilizer at least one of your applications every year. Organics feed the microbes and keep the population more normal.

Thanks for the watering tips! I’ve found that saturating where my dog urinates with water immediately after she goes keeps her from killing the grass. I must have missed one spot so I’ll try the sugar trick. There were also some bare spots existing when I moved in. I’ve been trying to figure out how often to water and may well be over watering.

Imperial Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, oscillator sprinkler (full sweep) and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and for the most part, in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Metric Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 3 cm all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps from 33-38 deep water once per week. With temps from 25-32 deep water once every 2 weeks. With temps from 21-24 deep water once every 3 weeks. With temps below 21, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. In the USA this deep and infrequent schedule works in Phoenix and in Vermont (for Oz think Hobart to Darwin including Alice Springs), so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.