To answer OP's questions:
1) I think Kim Davis's actions are legally indefensible. She has no legal grounds for refusing to issue those licenses. Her attorneys (from Liberty Counsel) have a history of losing cases and giving their clients bad advice--I suspect this has exacerbated the problem. If she has a sincerely held religious belief that keeps her from issuing the licenses, fine. But she shouldn't interfere with her deputies, who have no such reservations. Judge Bunning gave her this option yesterday and she refused. This is where I start to think it is more about impeding the implementation of the SCOTUS ruling than anything else.
Also, before she was jailed, she wasn't even issuing licenses to straight couples. How can she say is refusing to issue those based on religious beliefs? Again, I think this was bad advice from shady attorneys. She is paid 80k a year and she won't even do the noncontroversial half of her job. Not a good look.
Don't work there so I can't answer, but you can deduce from the media coverage that it is not fun. I have heard that all the employees, even those who do not work in the clerk's office, have to endure people screaming at them as they walk into work.
Kim Davis only won her election in January by a slim margin. I don't know if this has helped her or hurt her in Rowan County. I hate to say it, but I think she would probably win an election if one were held right now, but I hope I'm wrong.
A lot of people in Kentucky share Davis's views on marriage (over half don't support gay marriage, according to the last poll I saw). However, there are a lot more progressive-minded people in Lexington and Louisville. Also, almost every young Kentuckian I have come into contact with and had occasion to discuss the topic with support equal rights for homosexuals. I am very proud of my state and many of the people here. This is just one of those issues that still divides us, especially the younger vs the older generations.
I don't know Kim Davis personally, but everything I have heard indicates that she will not relent. She has so much attention on her now that I think she really feels like she has her back up against a wall. So many people are making her out to be a martyr and I think that will help fuel her resolve.