You are probably OK, and some termite parts could have been tracked inside. You have spent a lot of time on your posting and have a lot of detailed questions.

This is not a real active forum, yet someone with expertise on termites might respond, it could take many days, though.

You are more likely to find timely advice on websites such as:
http://www2.ca.uky.edu/entomology/entfacts/ef604.asp

A lot would depend on which species of termite they are. The majority of species are grass eaters. Although they can leave trails/grooves in timber where they build their nest. But there are wood eaters so it pays to be vigilant.

After the mating flight the young queens are fertilised for life. They find a secure dark place and lay eggs. When the young mature they take on all the duties of collecting food, tending the queen and new brood, defense and expansion of the nest. Of all the termites that go on the mating flight and then are attracted to lights very few if any manage to establish a new colony. They are an important food source for a lot of creatures. Any survivors are usually only those that get back to the original nest. But, there can be exceptions.

Because termites construct their own controlled climate nests and tunnel system it doesn't matter if the outside environment is dry. They prefer high humidity and get it in the nest and tunnels.

To stop them coming to your lights you can use yellow fluorescent tubes. You only need to use them on the few nights a year when the mating flights are on.

When living in a termite area it's a good idea to get a professional to check the house from time to time. Houses should be built to make it difficult for termites to infest. Of course, that doesn't always happen. Good luck with it.

Are you sure that they are even termites? Ants swarm just like termites and when the mating rituals are over, they leave little piles of wings and carcasses all over.

If you get a positive identification (take some to your local extension office) of termites, you'll need to call a qualified extermination company (bonded and insured) to investigate. They will be able to take care of the problem far more efficiently AND safer than you with your household sprays.