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You are correct, it is likely growing from the root stock. There is not way to know the citrus variety of root stock; it is likely a rough lemon or a sweet orange.

It's tough losing a plant, let alone a lovely Meyer Lemon Tree.

Yellowing leaves can indicate watering issues or nutrient issues.

You should use a fertilizer that is specific to Citrus to meet it's needs.

These links have more information.

https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm
https://www.gardeningknowhow.com/edible/fruits/citrus/tip-on-water-requirements-for-citrus-trees.htm

This will need as much light as you can possibly give it. Not having enough light will keep it from fruiting properly. If you do not have a reliable light source during the winter, then you might want to consider about 200 watts of horticultural lighting to supplement. Also, I recommend keeping dolomitic lime and iron sulfate handy. You will want to use this 2 to 4 times per year. This will prevent many problems before they start.

Also, just make sure to water only when the soil is almost completely dry. This will prevent soil infections, and keep the plant at its happiest.

You should probably just wash it off. One possibility is honeydew, which is a sticky substance secreted by sap-sucking insects like aphids and scale bugs. It can get on fruit, leaves, and everywhere else:
https://www.gardeningknowhow.com/garden-how-to/info/what-is-honeydew.htm

The smaller yellow ones are dropping off because the plant cannot support them. Make sure to keep the soil moist and apply iron sulfate and dolomitic lime around the tree. Make sure that the fertilizer doesn't have a lot of nitrogen. This can inhibit fruiting. They will need heavier amounts of phosphorous and potassium at this time. It will take some time for it to recover from transplant.

This article will give you more information on the care of these: https://www.google.com/url?q=https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm&sa=U&ved=0ahUKEwif597Bgc_aAhWE1lMKHd7zBbkQFggFMAA&client=internal-uds-cse&cx=009296322515861343460:jftykenwinc&usg=AOvVaw28Pl073Xmvj3ZpEKRW_scY

The lemon juice should still be good, as long as the fruit smells good when you cut it open. If the fruit is shriveled up or overly squishy, it might either have gone bad or have little juice left. Otherwise, should be fine.