IPhone 6 unable to login to iCloud

Question

I made a mistake that has cost me a lot of time and research without much success in finding a solution. Here's what I did and the problem I can't seem to get around.
I am on iPhone 6 iOS 8.0.2, 128GB storage with 100GB available (haven't moved photos into new phone yet)
I was having an issue, I thought, whereas the phone auto locks immediately and I like to keep this feature at 2-3 minutes in the previous iOS, for messaging while at work or home, I don't require it to lock immediately. Anyway, I thought perhaps the feature was tied to fingerprint combined with passcode so I disabled passcode and tried to figure out a way to create the auto lock wait a while, the "immediate" lock feature is not able to be selected nor deselected, it's just checked. I placed my passcode back into the phone and that somehow turned off my voice mail and removed my iCloud data. I tried logging into iCloud many, Many times, I know my password, I'm logged in with my iPad and on computers, iTunes recognizes the iPhone 6 as my primary and authorized iPhone, it backs it up and refreshes the iOS fine. I called the wireless provider and they created a new password for my voicemail and stated that I won't have to use it unless I travel to another country. fine. Voice mails poured in. I researched here to figure out what is going on with my Apple ID and no one has had this specific issue, mostly people are talking about installing iOS and having not enough space. I am unable to log into iCloud on my iPhone 6 and the error reads: "Authentication Failed" "A server error has occurred" and that's it. The error pop-up has an "Ok" button so I click it. I can see my picture, my email and information looks like it is ok though acting strangely.
Steps to reproduce, I guess remove passcode and apply a new passcode is how this happened, even though I used the same passcode when I did this. Go to "iCloud" in "Settings" then select your account to "Log In" to "Apple ID" for iCloud management on the iPhone 6. Enter password correctly, it loops around and asks for it again then states that I have it wrong and a server error occurs.
Days have passed by and I was just now able to fix the voice mail though I am unable to correct the iCloud loop.
I have 2 step verification though I am unsure where I set this up, perhaps if I remove 2 step verification?
I am not using iCloud Drive yet as I rely on Macs (computers) to be the hub of my information, need Yosemite.
I do not backup to iCloud, all other options in the .Mac account are always selected.
I backed up the iPhone 6 prior to this issue and attempted to correct using a backup and that did not work either.
Any and all help is appreciated.
Thanks.

Answer 1

I am assuming you are speaking of the October update? It most likely won't have Apple Pay just yet (which I'm excited to use).  I cannot wait for the Apple Pay updates as I believe they are launched with the watches, in the Spring or early 2015? This bug is annoying, I cannot manage my central IDENTIFICATION!
Following every step from Apple and from people here, thank you for replying, does not work, screenshots below show the errors and how they occur. I suspect that it's the two-part verification system.
I'm sure it will be fixed in the next update during the October (this month) event with the iPads, if new ones are released-lol
If you are reading this and have not had this issue, read the initial post I typed to see how this occurs. Basically, if you remove "Touch ID" and your "Passcode" then reapply, iCloud locks you out and gives an error as "Authentication Error - A Server Error Occurred" - This is constant and not intermittent, screenshot is provided from my phone (blurred out identifiable data).
Here is how the iCloud loop occurs AFTER the Touch ID / Passcode change causing this bug;
1. select your account:
2.  Enter your password; 3. iCloud Requires Additional Verification
Enter Password again
LOOP Error Occurs
I tried this and it did not work. Thank you for your reply.
RogueFive wrote:
I have just used Apple Support Chat and they seem to have resolved my problem.
Basically I had to close down every app by double tapping the home button and sliding each app up to close it. Then turn the phone off and on again.
Simple.
Seems to have sorted my problem and may sort yours. If not I suggest to contact them directly or visit an Apple store where I am sure they can help