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This is a lack of nitrogen that causes this. It is best to fertilize in early spring each year. Now would be a good time to do so.

Alternatively, it could be a pH issue in the soil. This can be corrected using, both, dolomitic lime and iron sulfate in the soil. Follow the instructions as per the package. This can make nitrogen unavailable if the pH of the soil is too high.

First, you will need to find out where the graft point is on the tree. This is likely growing below that graft knot. If this is the case, it is likely to be a wild citrus, and not produce an edible fruit. It is best to take a cutting from the top fruiting portion of the tree. This will ensure that your tree will fruit within the first few years, as it is the same age as the parent tree.

If you still want to take this small shoot, then you can still do so, but I would also take a branch from the top if you can, as well.

This can be done by snipping the branch at an angle directly at a leaf node. Dip this in honey, or a rooting hormone of your choice. You can put it into some good potting soil, and keep it moist but not wet. The cutting will practically root itself in a week or two.

Many citrus, by the time they are able to bear fruit, will no longer have thorns. Determining the type based on this alone would be close to impossible. If you know for sure that the tree is not a grafted tree, and you know the age of it and it should not be able to fruit yet, then this can narrow down the possibilities but this trait doesn't indicate a certain species. You will have to wait for fruit to determine that.

I, also, notice that there seems to be a pH imbalance from the crinkling and curling of leaves. This will need to be corrected with dolomitic lime and iron sulfate.

It is much easier to peel the outer skin off. Start with a razor, or very sharp knife to pry into the tip of the seed shell. Then, once you get enough to pull, peel the outer coating off.

Once you have your seeds, you can plant then straight into soil, or put them into a damp paper towel (not soaking wet) and into a bag over a few days.

With water? Yes. There should be no harm in doing this.

Can you include photos? This could be that the tree is not old enough to bear fruit quite yet. It could also be that it is lacking fertilization. There are many citrus fertilizers that you can apply at about this time.