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Some leaf drop is normal. Excess leaf drop can be due to uneven watering, pests, and disease.
Citrus need full sunlight and warm temperatures, so an indoor setting is not ideal.

You can use a grow light to increase the light.

https://www.gardeningknowhow.com/edible/fruits/grapefruit/growing-grapefruit.htm
https://www.gardeningknowhow.com/edible/fruits/grapefruit/grapefruit-tree-not-producing.htm

There are several possibilities for the death of your grapefruit tree. Diagnosis would require more information on the site, growing conditions, your soil fertility/fertilization, water and pest management.
In Florida, HLB (citrus greening disease) is a real possibility. It's a bacterial disease spread by an insect vector, the asian citrus psyllid.
Some other common citrus issues that are serious enough to cause mortality are water related, too much or too little. Severe water deficit can be fatal; over-watering can cause root and crown rot.
Other possibilities include root cutting or compaction from construction disturbance, sewer repair excavation, weed killer or other chemical contamination of the soil or foliar crown, paint or fuel spills.

They will grow, and they may or may not produce fruit. It will take around 6 years or more before you will be able to find out. It will not be a grapefruit, however. It will revert back to one of the parents, or even further back. This can often be edible, but much more often it is not.

That does not mean that you can't grow it and appreciate it for what it is, but you can't have any expectations of the tree. It is going to be a total mystery.

Also, there will likely be thorns... Lots of them and far too many to count. As long as you can cope with that, then there is not any reason not to keep them alive.

Their care will be similar to any citrus, so I will include our articles on citrus here: https://www.gardeningknowhow.com/edible/fruits/citrus

Yes that's a good idea. In nature the fallen leaves provide soil nutrient replenishment, so you are following the same principle with the help of your blender. But it's not enough. Some nutrients are leached out of the soil with watering, and some are used by the plant metabolism, so a general purpose or citrus specific fertilizer is needed as well.

This ,typically, happens when there is too much nitrogen present in the soil, or too little phosphorus. Adding more phosphorus will help the plant take less nitrogen up. Recursively, too much nitrogen affects the uptake of phosphorus. Here is an article that will explain in more detail:

https://www.gardeningknowhow.com/edible/fruits/citrus/citrus-fruit-thick-rind.htm

The condition is possibly "Phytophthora gummosis" a fungus-like disease organism that causes the exuations. See the 'management' section in this UC article.
http://ipm.ucanr.edu/PMG/r107100411.html

There is one fungicide that I know of that is labeled for phytophthora disease, Subdue Maxx or the generic equivalent:
https://www.domyown.com/mefenoxam-aq-fungicide-p-16650.html

It only takes a quarter ounce per gallon of water for a soil drench solution. But the minimum purchase is a quart, so it's kind of expensive.