Refinancing a 30-year mortgage?

We’re at 5.85% right now. Initial 240k loan down to 200k in seven years. Credit score 720+. No missed payments. Looking to refinance but have a few questions:
1) Are there any websites that give ONLY currently available interest rates? I signed up online for a few quotes and now have no less than 8 people calling and emailing me. All I want to do is browse sites and compare rates, is that so much to ask? Oh, and idiots that send links to sites that are basically the same thing I did initially, please save your time and mine and don’t send them… I won’t be clicking on them.
2) My wife is balking at paying around 3k to refinance. If we take our interest rate down a single point to 4.85% or somewhere near this, over the long haul we’ll save several thousand dollars. The main reason for her balk is that my job situation isn’t as rosy as it once was. I’m working now but was laid off last year after being with a fortune 500 company for nearly 8 years… and my particular industry (sales) is going to change toward something other than good in the future (not as much need for my type of sales).
3) I’ve heard an advertisement on the radio about loans and refinancing things that mention a lot about “… as low as 2%” and “… no refinance charges.” I’m assuming those are the variable rate-type offers that rise to some crazy rate after 5 or so years… right?
4) I’m a veteran. Are the rates offered to vets that much different than what’s offered to the general public? I don’t think they are. There may be some breaks when it comes to purchasing a new home
but otherwise it’s looking like there’s really not that great a deal for vets.
5) Remember, please, don’t reply with idiotic links to idiotic sites. If I deem a site worthy, I’ll visit it.

Thanks for any/all information.

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