Unfortunately, iOS 5.1.1 is no longer being signed by Apple.
Basically, Apple provides a digital signature to iTunes when you try to restore a firmware. If the signature isn't provided, you're unable to restore because Apple only signs the most current version of the firmware for the device you're using.
The Dev-Team Blog says this about downgrading an iPhone 4S to 5.x:
iPad3, i4S owners will always be able to RE-restore the current 5.x OS that's already on their device. So if you're at 5.1.1 when the window closes (and you've saved your blobs), you'll always be able to RE-restore to 5.1.1 again. This makes the 5.1.1 jailbreak a lot less fragile - you don't have to worry about messing up your install with funky extensions or getting into a boot loop, because you can always RE-restore from 5.1.1 to 5.1.1 again (or from 5.0.1 to 5.0.1 again, etc). But once you fall off the 5.x train by restoring to 6.x, you'll be stuck there until the next jailbreak.
So it looks like you're stuck on iOS 6 for now.
Regarding unlocking, your best bet is to contact Verizon. There may be a fee required before they'll unlock your phone, if they do.
I think I found the Answer I was looking for in How U.S. Carriers Fool You Into Thinking Your iPhone 4S Is Unlocked
Short answer "You can't do it!" If your phone is CDMA, its permanently locked to its CDMA network of origin.
Unlocking your Iphone 4S
Among the three major carriers operating in the U.S., only one, AT&T, will not unlock any iPhone. Because I purchased a Verizon-designated handset, the following information relates to those customers that purchase Verizon iPhones, but the technology and result is the same for any carrier.
When I called Verizon tech support to unlock my phone prior to leaving the U.S., I was told that I had to have a foreign SIM card installed in order to complete the process and that the phone would have to log in to the Verizon network on WiFi. The reason for this procedure is that the phone must validate the foreign SIM.
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So I stopped in at an Apple store in London. We logged into a WiFi network, installed a micro-SIM card from a carrier in England, and within about thirty seconds, the phone was unlocked because Verizon had already unlocked the phone at their end before I left the U.S. For the rest of my travels overseas, it worked flawlessly and provided essentially the same options that are available on any other dual-mode or GSM-only device.
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Four different iPhone 4S versions
When I returned to the U.S., I wanted to confirm that my Verizon iPhone could be ported to another carrier, whether CDMA or GSM. This was the intent of Apple when they designed the 4S: every phone is the same and will work on virtually any carrier in the world.
So, I contacted a regional GSM carrier in the Midwest that has roaming agreements with AT&T and T-Mobile. The carrier was kind enough to provide a micro-SIM card for testing in my iPhone. What I found may infuriate customers who have purchased expensive iPhones from one of the three carriers in the U.S. but at some point decide to switch to another provider because of poor coverage, customer service, or pricing.
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Sitting in South Dakota, I replaced my Verizon SIM with the Longlines Wireless chip. The phone indicated that the SIM was not recognized by the phone and required its removal and device reboot. I contacted Verizon global support to confirm my suspicions. They advised that indeed their phones were locked as against any other carrier in the United States, and that the term “unlock” only applied to overseas carriers.
I next inserted my UK SIM card into the phone, and it logged into AT&T without issue, which confirmed what Verizon told me. I then interviewed managers at three different Apple corporate stores to confirm issues with regard to unlocking.
What consumers need to understand is that there are actually four different versions of the iPhone 4S: Verizon, Sprint, AT&T, and Apple. Only the Apple phone, available from their stores or on-line, is fully unlocked and can be used on any carrier outside the United States. The other phones are permanently locked and cannot ever be used on another carrier in the U.S. Even if you spend $800 for an unlocked phone as I did and dedicate it to a single U.S. carrier, you are locked into that carrier forever if you want to keep using the iPhone. Neither Apple or the other carriers will fully unlock your carrier phone.
Best Answer
Verizon will unlock the phone for global use only, provided you've been a customer in good standing for at least 60 days. Otherwise, they will refuse to unlock it, and under no circumstances will they unlock it for domestic use.
Alternatively, you may find unlocking services on eBay, but these aren't as popular for Verizon phones as they are for AT&T.
There are no "Ultrasn0w"-type software unlocks anymore, so going through official channels is the only option, unfortunately.