Will low power mode influence my facetime connectivity (speed and stability) or whatsapp messaging system?
Considering according to Apple the low power setting affects 
"Background app refresh
Automatic downloads
Wi-Fi associations"

By reducing or disabling these features,

Then yes it will be affected, your WhatsApp won't update its content unless you have it open as the app you're using. FaceTime should still remain as good though on cellular networks but if you're moving around while connected to a wifi network you may have performance issues if you stray too far away while low power mode is on.

Source: https://support.apple.com/en-au/HT205234

Also further info on back group app refresh here: "Use Background App Refresh" https://support.apple.com/en-au/HT202070