Hello - We have been hearing gurlging sounds in our kitchen sink, bathtub, toilet, etc. Now this morning after my shower I went downstairs in our basement and found about 3 inches of clean (not sewage) water in our washing machine. What is going on and how do I fix it?

The gurgle is caused by a blocked roof vents that the disease snake. Snake both the kitchen and the bathroom lavatory roof vents. Put out enough snake to reach the base and 15 feet more.
Your washer sounds like a faulty inlet valve, This would be appliance repair, Good luck, Tom