I have an Ethan Allen mahogany dining table that needs a good cleaning

Murphy's Oil Soap is great for cleaning wood. What it won't do is repair a damaged finish. I would suggest cleaning well using the oil soap then reevaluate. You may have to refinish the top especially if the damage was caused by heat or the stains have penetrated the surface.

formby's liquid gold. if the heat rings are white look at a few videos on how to remove white rings from wood. it requires a thin cloth and a clothes iron.

The oil polish I use is called Old English. It is a cleaner but also helps restore the wood to its color and helps oil it. It comes in dark or light so you should find what you need with your mahogany. It sounds like a beautiful table. The mahogany I've seen is dark. You might give it a try. It is sold where furniture polish is sold. I keep it on hand for minor scratches and for cleaning my tables and cabinets twice a year.

http://www.thefurnitureconnoisseur.com

Hi. Ethan Allen provides this guide to clean and maintain various pieces of their furniture. https://www.ethanallen.com/on/demandware.static/Sites-ethanallen-us-Site/Sites-ethanallen-us-Library/en_US/v1377807488810/pdf/EthanAllen_UseCare.pdf

Howard's Restore-a-finish will do the job. It can be purchased at big box stores and paint stores in various colors. It is quick and easy and there are you tube videos.

Mayo on the water rings...