Sorry that the instantaneous pace was erratic. It comes from Apple's GPS or Pedometer systems and neither are great. If you press the watch screen hard and tap Settings and then Pace then you will find various ways to improve it. Tap Current Pace to choose between GPS or Pedometer, and there is also an option to smooth the values (which I added because of the erratic instantaneous pace).
Alternatively you could use a rolling pace instead. There are 3 rolling pace metrics, so you can display 3 different time or distance windows at once whilst deciding which window works for you. The longer the window then the more accurate the pace but the less responsive it is, and vice-versa.
In the next version I have added an option to determine the pace from Apple's distance estimates, which seems less erratic.
In terms of the heart rate not varying often, this is an issue with the watch sensor which affects some people during colder weather when the blood vessels are further from the surface of the skin, although it can happen at any time. There is nothing the app can do about it.
It varies from person to person and some people use external monitors during the colder months. Apple have advice on it here:
https://support.apple.com/en-gb/HT207941#heartrate