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Unfortunately, this method for germinating avocado seeds is purely for novelty and rarely leads to a healthy, mature tree. At this point, the infection is likely too far progressed, and you could have another tree growth, and in much better condition, before you could get this one to recover.

The best method for starting avocados will be to direct sow in soil, and put under lighting immediately. A healthy seedling will have about 6 leaves by the time it about a foot tall. Stretching, and low leaf count will be a result of lack of lighting.

An alternative method for starting will be to wrap the seed in a slightly moist paper towel and place in a ziploc bag in a drawer for a few weeks. Check it occasionally for germination, and plant when it is showing signs of germination.

This article will give you more information on the care of avocado trees: https://www.gardeningknowhow.com/edible/fruits/avocado/avocado-tree-growing.htm

Sure! You can plant a pit from a store bought avocado, but they don't normally produce a very tasty fruit from seed. They must be grafted from a variety known to fruit well. Your seed-planted tree will still flourish, but it may not yield anything edible or tasty.

It is best to graft a new top onto your seedling's rootstock, or to purchase a tree that has already been through this procedure. This will ensure that you get a good fruit and that the tree is robust and healthy. They usually fruit within just a couple of years from graft, versus a seed which can take many years to fruit, if it does at all.

This article will help you to grow these trees: https://www.gardeningknowhow.com/edible/fruits/avocado/avocado-tree-growing.htm

Seed planted avocados will not have the same fruit as the one that it came from. Sometimes, they won't even fruit at all! To obtain fruit, the first thing on the checklist is that you have a known fruit producing variety that is grafted to a viable rootstock.

Of course, there are other factors as well. This article will explain in more detail: https://www.gardeningknowhow.com/edible/fruits/avocado/avocado-tree-with-no-fruit.htm

It may be the type of avocado that you have. Avocados take around 9 months to ripen fully, so if it is before this timeframe, then they will be far from ripe. Knowing when to harvest is not necessarily easy. This article will help: https://www.gardeningknowhow.com/edible/fruits/avocado/tips-for-picking-avocados.htm

Unfortunately, without photos, I cannot ID the tree in question.

There are too many varieties to know what kind you have but here is a trick to remove the fruit. One idea is to split the fruit in half by cutting around the seed in the middle, width-wise, not length-wise. Once the fruit is halved, slip a knife blade between the skin and the fruit all the way around to free the fruit from the skin. You may want to check with a culinary website for more tricks.
Here's an article you may enjoy: https://www.gardeningknowhow.com/edible/fruits/avocado/tips-for-picking-avocados.htm