I think it's an ordinary Kalanchoe blossfeldiana - it needs a bigger, proper pot with drainage holes, and cutting back to about 1-2 inches all over. Your grandmother might remember it as a small plant bought in flower originally, perhaps. It's grown like this because it does not have enough root room and is unable to put out new stems and be the bushy ...
It's more likely algal growth because of the glass pot - in sun, algal growth thrives, but will appear even in shade. Its unlikely to cause harm to the plants, but it will proliferate over time, and likely indicates the soil is too damp, especailly if the pot does not have drainage holes. If there are no drainage holes, it would be better to repot into ...
You are correct; there is not enough light to support robust growth for this plant. In order to stop the etiolated growth and pieces falling off you'll have to give it the appropriate amount of light.
If that's not possible, don't worry about it, it will continue to grow and pieces will fall off occasionally. As long as you like it, it's OK.
No, this is not aloe-vera however one of its type and comes under category of succulent.
These types of plants need very less water, sun-light and maintenance.
You can check about these types of plant at this link. and here.
Hope this helps.
See the wikipedia entry for Haworthiopsis attenuata - in the description section there is an attempt to draw a distinction between the two species based on where the tubercles occur on the leaves, along with rather minute details about the leaf shape.
Both species require good drainage, with more water in the heat of summer than in winter, and good bright ...
I have raised almost every kind of cactus and succulents in my sixty years of loving them. In almost every case I have found that watering once a month is plenty and you will never have one rot, or root rot. If you’re somewhere very hot you can step it up but it’s been a never fail rule for me. I use the first day of the month so I don’t forget.
Aeonium arboreum, possibly the variety 'Zwartkop' or 'atropurpureum' so no, it does not need a shallow pot, these can grow up to a metre or more. You won't be sure its Zwartkop until it's had some sun exposure - the leaves lose their black coloration without it, although in very hot and sunny places, they actually prefer a relatively shady spot. I wouldn't ...
This is peperomia obtusifolia, AKA baby rubber plant.
They can grow in water too and need to have only few nodes in water.
They like moderate to bright indirect light and are very resilient to pests. Soil needs to dry out completely before watering.
Image from Plantsrescew: