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Redbud has a tap root that can go quite deep if soil type and conditions are right. This is why the Redbuds are considered extremely stable in inclement weather for a smaller tree. Their surface roots can extent at least as far as its canopy is wide (10' to 15'. They have shallow surface roots that are thin and not considered invasive or aggressive. This small tree can be planted near patios, decks, and foundations without problems. As far as the tape root causing any problems; all trees are opportunistic and will, if exposed to the water provided by a leaking pipe, exploit this resource. A distance of 15' to 20' from septic tanks, drainage systems etc. would be wise.

It is a possibility to prune these shrubs to keep them manageable. As will all trees and shrubs, you will want to be mindful of what you are planting near. Although these shrubs are smaller in stature, the roots could still penetrate lines, and under asphalt. Here is a link that will help:https://www.gardeningknowhow.com/ornamental/trees/redbud/cutting-back-redbud-trees.htm

Yes, fall is a good time to plant trees. Make sure to dig the hole the same depth as the plant but 3 times wider. The "flare" at the end of the trunk should be above ground. I use a hand cultivator with blunt tines to tease out the roots. You must avoid planting roots that circle the root base. It is better to prune a circling root than allow it to curl in the planting hole. Firm the dirt with a foot while back-filling. Give it an inch of water a week all the way through fall. The roots keep working after leaf drop until the ground freezes.

Unfortunately, unless you specifically planted a red variety, then most are green. These will continue to remain green, or yellow in fall. Make sure the variety you planted is, in fact, a red redbud.

Eastern redbud is native in WV. It prefers slightly alkaline soils but also grows in the more acidic New England area. The seeds need pre-treatment to germinate. The technic and plant care is discussed here: https://plants.usda.gov/factsheet/pdf/fs_ceca4.pdf
There are YouTube videos on stratification.

There is not much care required for these trees. They are pretty hardy. Any winter care would depend on where you live, but they can survive just about anywhere. This link will give you more ideas on the care of these trees: https://www.gardeningknowhow.com/ornamental/trees/redbud/caring-for-redbud-trees.htm