I have had plumbers and the city waste department but no help they tell me it is the others problem. My downstairs 3 toilets start gurgling, then the water level drops then rises quickly causing over flow. My shower and tub downstairs then fill up. The city guy came this morning and told me the plumber needs to find my catch basin? The plumbers have used the snake approach and nothing there so they tell me that it is a problem at the street. I see a pattern after heavy rain storms. How do I find the covered basin in my yard. I called DOTTIE to come mark my yard for sewage, gas, cable, phone,and electricity. I thought that might be a start. We bought this 25 year old house 4 years ago so I also called the last renovation architect for his inpute. Help!! How do I check for the methane gas?

The building department keeps records of all sewer raisers. Contact them.
If you smell sewer gas then you have methane in your home but most likely not in sufficient quantity to harm you. You may have to install a running trap,(see image) in the line from the house to the street to trap the smell.
Good luck, Tom