16. How do you think this deity represents the values of their pantheon and cultural origins?Hospitality was quite important to the ancient Greeks, both being a good host, and a good guest. While there are perhaps some other deities who deal more directly with this (Zeus Xenios, perhaps?), I feel that Hestia plays a role here, too, in providing the guest with food and drink, as well as a safe place.
Hestia likely also demonstrates the importance of family and of a peaceful home, and perhaps the value of the extended community.
17. How does this deity relate to other gods and other pantheons?
Hestia was frequently worshiped alongside quite a few other Greek deities, including Apollon, Poseidon, Zeus, Hermes, Hekate, and others, but unlike some ancient deities it seems she wasn't really worshiped outside her pantheon, or not that I have seen, in any case.