iPhone 5 Battery - Help me diagnose issue

I'm having a weird issue with my iPhone 5, that I think is related to the battery, but might be something else.

Symptoms

• The battery indicator is wrong. It sticks to the value it fetches when rebooting the phone. Currently, it shows 58% regardless that it's been charging for hours. If I reboot it, however, I get an accurate value, and it sticks to that one.
• I get the following error message in the Console when plugging it to Xcode:

    CLTM[14] : CLTM: partial sensors: count 5156, current 39fffe, mask 1b, expected 1b
    CLTM[14] : CLTM: Could not get event from temperature service
    CLTM[14] : CLTM: Could not get value for gas gauge battery
    CLTM[14] : CLTM: Could not get event from temperature service
    CLTM[14] : CLTM: Could not get value for gas gauge battery
    CLTM[14] : CLTM: Could not get event from temperature service
    CLTM[14] : CLTM: Could not get value for gas gauge battery
    CLTM[14] : CLTM: Could not get event from temperature service
    CLTM[14] : CLTM: Could not get value for gas gauge battery
    CLTM[14] : CLTM: partial sensors: count 5160, current 39fffe, mask 1b, expected 1b

The value in partial sensors: count XX increases as the iPhone runs.

• After rebooting, with the battery too charged or too discharged, the iPhone enters a reboot loop, where it will reboot every 5 minutes. Eventually, when the battery reaches 75% or so, it remains on. At that point, I can use it "normally", with a wrong battery indicator.

Here's the tricky thing: I live in Argentina where the iPhone is not officially for sale, and no authorised services are available. I got it when travelling to the US.

I can easily have the battery replaced (parts are available and not too expensive), but if it's not the battery (maybe the charging circuit?). Since the service is not authorised, however, I'm reluctant to have them open my iPhone if it won't solve the issue.

My question(s) therefore are:

• Did anyone experience something like this? If so, was the problem the battery?
• Does anyone know what CLTM in the Console log could mean?
• Is the battery level meter part of the battery itself (and therefore will be fixed when changing the battery) or is it a separate thing?

Solution 1:

It might not help the OP, but Apple has battery replacement program for iPhone 5. You can check eligibility on Apple site

Apple has determined that a very small percentage of iPhone 5 devices may suddenly experience shorter battery life or need to be charged more frequently. The affected iPhone 5 devices were sold between September 2012 and January 2013 and fall within a limited serial number range. (...)

The program covers affected iPhone 5 batteries for two years after the first retail sale of the unit or until March 1, 2015, whichever provides longer coverage.