Gabriel,
Welcome to this forum. You will get plenty of answers to your questions, so ask away.
Now, to answer your questions. You mention that it would be great to keep your figs "indoors" for the cooler months in Connecticut. Where, indoors? Do you plan on keeping them from going into dormancy, and actively growing in some sun-room, or will you let them go dormant? Unless you can provide them with very bright sun, (think, greenhouse conditions) all day, you will have weak, growth that may die off when plants go back outside as the weather warms. Even if you can provide adequate light, the figs will have to be acclimated to the outside conditions, and be slowly moved into full sun. You still might lose all the leaves, and the trees will have to re-grow new foliage. Storing them in a dormant condition is far easier, and the resulting flush of new growth, will be much healthier and more productive. An unheated garage or storage shed will answer nicely.
A forum search will yield many postings on overwintering figs.
Good luck.
Frank