The initial response to the 3 yr old OP answers your first question. The green lights are the Heart Rate monitor which can be turned of under Settings-Sensors-Wrist Heart Rate. Obviously you will not then get HR data! Neither of these will make much substantial difference in battery life likely (under normal conditions). Comparing battery between watch models is not likely useful and if you are having substantial battery drain compared to other 5X+ users then you may need to look elsewhere for an issue (after searching the forum).
If you do not want to use Wi-Fi on your Fenix 5 series watch, do not connect it to Wi-Fi. You always have the ability to remove a Wi-Fi network you have prior saved and connected to on your watch.
- Go to Settings > Wi-Fi on your watch and remove the network.