Just a few of points:
Signage - this will be changed over time and additional signage implemented over the coming weeks. The decision was made to open and then review signage. Changes will gradually appear as the overall TTS improvement project nears completion later in the summer.
Walkway times - the times are generally exaggerated across the terminal so that customers always allow adequate time to reach their gate with stops if required and without the need to rush. So you are correct in that while the signage says 20 mins to T5C, it can easily be done in around 10, depending on the individual. By stating 20 minutes, customers can plan accordingly.
Moving walkways - Heathrow is aware of these and it was expected that there may be initial snags as the equipment beds in. Also, at least one is planned to allow for the operational maintenance team to get a better understanding of the new equipment (different make to existing ones).
I do agree that the walkways are a good way to avoid the crowds and have some quiet time to yourself. Plus the temperature is more consistent than the rest of the terminal ;-).