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Remove the secondary stem, allow the tree to grow up with only the one primary stem. Fertilize with a complete organic fertilizer.

Don't over water, avocados are susceptible to root and crown rot. Water deeply and then let it dry out in between.

Avocado is a large growing tree and can take several years before it produces any fruit. They are also frost sensitive. Be sure you have the pot on wheels so you can move it easily.

Here is general care:
https://www.gardeningknowhow.com/edible/fruits/avocado/avocado-tree-growing.htm
https://www.gardeningknowhow.com/edible/fruits/avocado/cold-tolerant-avocado-trees.htm

They can be. It won't hurt them as long as they are well established and healthy. Just don't go too far above that, or you risk infection to the crown and bark.

This article will help you with the care of the tree in container: https://www.gardeningknowhow.com/edible/fruits/avocado/indoor-avocado-plant-care.htm

That is one of countless "White Rot" fungi! They are very hard to ID without seeing the fruiting body in question. Leaving it can harm the tree in the case of a parasitic fungus, or if it is simply needing a host and is not detrimental, then it will cause no harm.

Since it is very difficult to pin down without a fruiting body, it is best to assume that it will kill your tree.

I would remove the infected branches, and treat with a fungicide to be safe.

This article will help : https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

This University website will explain further: http://ipm.ucanr.edu/PMG/PESTNOTES/pn74109.html

It looks like the classic symptoms of overwatering, or a pH swing. These are definitely the early signs of root rot.

From here, you will need to treat with a fungicide, and provide the tree with full sun (meaning higher than window lighting can give) or at least 200 watts of horticultural lighting- Whichever is easier.

These articles will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/edible/fruits/avocado/indoor-avocado-plant-care.htm

The only way that I could see this happening will be some kind of circular metal barrier being build down very deep into the ground. However, without being able to access roots to keep them pruned, this will only last for a few years before the tree likely fails.

It is best to keep them in container to root prune when they need it, or they will overcrowd themselves.

What you can do is to plant a pot into the ground level with the ground at the top, then put the tree in a pot inside this pot. This is called pot-in-pot production.

This document form the UT extension will give you a good run down on pot-in-pot production: http://www.tnstate.edu/faculty/ablalock/documents/Pot-N-Pot.pdf

You can cut off about a third of the height and it should start to branch. When the branches reach about 8 inches you can pinch off the growing tips to further aid in branching.

https://www.gardeningknowhow.com/edible/fruits/avocado/pruning-avocado-trees.htm