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Use a good quality potting soil.
Here is a link with more information.

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

Unfortunately, no one had clearly identified it. It could possibly be mold or fungus. If the water isn't changed every 2-3 days, then the likelihood of contaminants such as mold, fungus or fermentation will increase.

The pit will eventually drop off. You seem to have a good root system going so I don't think I would worry too much. You can try wiping off that white secretion.

For more information on sprouting avocado pits, please visit the following link:
https://www.gardeningknowhow.com/special/children/sprouting-avocado-pits-how-to-root-an-avocado-seed.htm

The kind of insecticide you use depends on which insects are afflicting your avocado tree. I would recommend you read the following article for insect identification and course of treatment:
https://www.gardeningknowhow.com/edible/fruits/avocado/avocado-pests-and-diseases.htm

Squirrels, raccoons, opossums, field mice and rats will chew avocado fruit in any stage of development.

You can try filling drawstring mesh bags with mothballs or wrap mothballs in a cheesecloth secured with a rubber band. Hang the mothballs on the branches of the avocado tree. Replace the mothballs when they lose their scent.

To deter squirrels in the daytime you can dangle CDs in the branches. You can also try giving the squirrels an alternate food source located away from your tree to minimize the number of snatched avocados.

Here is an article with ideas on how to squirrel proof your fruit tree:
https://www.gardeningknowhow.com/edible/fruits/fegen/squirrel-proof-fruit-trees.htm

An article on raccoons:
https://www.gardeningknowhow.com/plant-problems/pests/animals/getting-rid-raccoons.htm

...and one on opossums:
https://www.gardeningknowhow.com/plant-problems/pests/animals/possum-control.htm

It appears that your Avocado plant needs more sunlight. Increase the light that your plant is receiving and as it grows more leaves you can began to pinch off to create a bushier plant.
Here is a link with care information.

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

From my research the root stock that is used for this Avocado is a seed grown root stock.
The chances of it bearing any fruit are extremely slim.

It would be best to start new.
Do some research on the best root stock for your growing zone.

https://www.gardeningknowhow.com/edible/fruits/avocado/avocado-tree-growing.htm

I did some research on fruit spotting bugs and the recommended means of organic control for them. The recommendation by some is to spray with pyrethrum and neem oil every 7 days, however, the frequency is really dictated by your insect activity. Mix two tablespoons or pyrethrum and two tablespoons of neem oil to 4.5 litres of water.