The apps need permission to the microphone for that and in background it would drain the battery and constantly show the microphone is accessed unless you are using an old android version. It is likely easy though to eavesdrop when the app is opened and using microphone is an expected functionality, and to pick up keywords and the sounds emitted from other sources to better know location and social graphs without GPS access.

Nowadays even calculators have terms of service and a privacy policy that is longer than many novels. Some probably have forced arbitration also.

Google itself as of this moment never did put adds on a lock screen, it is the manufacturer or third party apps who can do it. Some Realme and Xiaomi phones do it afaik and probably some other brands.