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Yes, thorns on citrus trees are totally normal and natural. You can cut them off if you are worried by them.

Meyer lemon should be hardy in your area. This article has advice on caring for them: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm

There is nothing wrong in pruning your trees back to keep them at the size you need. This article has more information on Meyer lemons: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm
If you want to keep them in containers, at some point you will either have to repot into larger pots, or root prune to keep them in the smaller ones. This article has more info: https://www.gardeningknowhow.com/ornamental/trees/tgen/growing-trees-in-containers.htm
If you end up keeping them outdoors, there are some steps you can take for winter protection. Remember to insulate the pots also: https://www.gardeningknowhow.com/plant-problems/environmental/protect-plants-in-freeze.htm

As you can see from this article, http://idtools.org/id/citrus/diseases/gallery.php?page=1
there are many disease that could strike your Meyer lemon. The first defense against diseases is always a healthy plant; use this article to double check your cultural practices: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm
I also recommend you take some samples of your diseased fruit, also any leaves that have spots on them, to the nearest county extension service, where they can analyze the problem and give you recommendation for treatment. This link will help you find the nearest office: https://www.gardeningknowhow.com/garden-how-to/info/what-is-extension-service.htm

Yes, totally natural. Here are a few more tips on growing Meyer lemons: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-meyer-lemons.htm

Whenever a plant, almost any kind of plant, is put through the stress of moving from one environment to another (never mind the stress of shipping,) it will drop leaves. What its doing is conserving its resources by pulling materials out of the old leaves in preparation for growing new leaves. It's hopeful that it can grow in its new environment. Be careful not to fertilize too much - fertilizer is not medicine, nor is it food. Plants make their own food from water, air, and sunlight. The minerals in the soil are more like the glue that holds things together, or the oil that keeps the engine running smoothly. If your lemon came in a growpot and soil, it was fertilized by the grower, you won't need to add fertilizer for 3 or 4 months; if it was bare root, the fertilizer you've added should be sufficient until next spring. Here's more information on Meyer lemons in pots: https://www.gardeningknowhow.com/edible/fruits/lemons/growing-lemon-trees-containers.htm
https://www.gardeningknowhow.com/edible/fruits/citrus/tip-on-water-requirements-for-citrus-trees.htm