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This could be the start of a fungal infection. I would advise using wettable sulfur and dolomitic lime around the area. This should take care of the infection.

This is, certainly, an old wive's tale. Human urine can harm a tree without the proper bacteria to break it down into something that is useful to the garden. It is best to leave anything that comes out of a human out of the garden.

This will depend on how cold it gets. Citrus can survive down a little below freezing, but they don't like it very much. If it remains above that, then I would say plant it. If it gets too cold, then I would say your best bet would be in container.

Here is an article that will help: https://www.gardeningknowhow.com/edible/fruits/lemons/how-to-grow-a-lemon-tree.htm

I would follow all package instructions, as many companies use different concentrations, and therefore, different measurements. It may not be a complete fertilizer, though. Citrus fertilizers are amended specifically for them, and I would recommend these over an all purpose. Depending on the age of the tree ,it may need a different NPK ratio.

Here is an article for more information on growing lemons in container: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-lemon-trees-containers.htm

I wouldn't be able to help you without a picture. If you could upload one, then I may be able to help. Could you describe the problem in more detail?

Usually, this is caused by a lack of phosphorus, or too much nitrogen. Both can cause the same symptoms. This article will help you in correcting the issue: https://www.gardeningknowhow.com/edible/fruits/citrus/citrus-fruit-thick-rind.htm