With charting it helps understand what is happening each cycle or over a period of time, so irregularities in length of cycles could be pinpointed on the over all picture. For example, a longer cycle might be contributed by ovulating later in the cycle, hence lengthening the cycle. From my understanding and readings the LP remains consistent.

Charts can also help practioners if you choose to seek medical assistance down the track.

I get most of my information from the following index of FAQs Trying To Conceive Q&A

Consistency is the key for temp taking... I take my temps orally, however some ladies find vaginally provides more accurate data.

Regarding varying waking times FF suggests...

How can I take my temperature when I have to get up in the middle of the night almost every night?
If you have to get up in the night and it is unavoidable, like having to take care of a small child, or if you have to go to the bathroom, just do the best you can. While some women notice rocky temperatures when they wake during the night, some women notice little impact. Take your temperature as close as you can to the same time each morning and choose a time that is likely to be when you have had the most sleep. For example, if your toddler wakes up every morning at 6 am, then take your temperature at that time, even if you go back to sleep. Try to avoid taking your temperature in the middle of the night, though, even if you seem to always get up at the same time in the middle of the night. Temperatures taken in the morning show a clearer biphasic curve and the time is more predictable.
Additionally,

Is it more important to take my temperature at the same time every day or after at least three hours of sleep?
Ideally, you will be able to take your temperature at both the same time and after at least three hours of sleep, but sometimes this is not possible. Do your best to meet the ideal as closely as possible. Whether or not you will have a more accurate temperature after sleeping the longest or at your usual wake-up time varies depending on your own unique metabolism. You will only really know after you have charted for several cycles and have experimented a little bit.