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You can remove the plastic if the cutting is growing and larger.
Just remember to keep the soil moist.

Not every cutting will be successful, that is why many gardeners plant several cuttings. When you do have success, it's always joyful!

Even though I am in the state of Tennessee, I LOVE to grow citrus. I myself have many, including blood oranges, and even Key lime. I know it is tricky growing them in container, but you can do it.

Now,I know you will be tempted to make your tree short from the get-go... But wait until it is about 3 foot tall, Then cut the top off to about 2 feet. You can even plant the top, and have a second tree.
Next, In container, these will want fertilization once ever couple of months. There are citrus fertilizers that take the guess work out of feeding them.
Now, as far as removing them from pot... Unless the temperatures stay above 20 or 30 degrees year round, I would suggest leaving them in the pot. All of mine are in 15 gallon pots, which they will remain in most of their life.

Here is an article on container citrus care: https://www.gardeningknowhow.com/edible/fruits/lime/potted-lime-trees.htm

This is common, especially with trees grown from seed. Often times, they come out nothing like their parents. You may, absolutely, graft from another tree. Just make sure to take from a tree that is already mature enough to fruit. You can also graft just about any other citrus to it, such as lemons, oranges, etc.

Here is an article that will give you information on grafting: https://www.gardeningknowhow.com/garden-how-to/propagation/grafting/

They are not really particular about soil type. I would not recommend high clay content, as this does not drain well.

Here is an article that will help: https://www.gardeningknowhow.com/edible/fruits/lime/lime-tree-tips-care-of-lime-trees.htm

Unfortunately, this is a difficult subject. Once they are inside the tree, they will do extensive damage. The best method of control is prevention, and once they get inside it can be hard to treat, often resulting in the death of the tree. Here is an article for more information: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-borer-insects.htm

That is strange. It is a possibility that the tree needs some fertilizer. How often do you feed it? I would recommend at the very least 1 or 2 times a year.

You may want to apply dolomitic lime, and iron sulphate to the soil. This will ensure the soil pH is about where it should be, then the iron sulfate will bring it down just a notch to exactly where it should be.

Yes you will cut this branch back all the way. Keep all new tiny shoots trimmed off near the base, as there will be new growth trying to replace it. Just focus on what is already on the tree.

Here is an article for more information on the care of the tree: https://www.gardeningknowhow.com/edible/fruits/lime/potted-lime-trees.htm