Explain how "scarcity is a central problem of economics as well as mother of all economic activities?"

Answer 1

Partially yes (only second part is true not the first part, though there can be exceptions)

Basic assumption in economics is that resources are limited or scare. Economics, at its core, is the study of how best to use those limited resources or in simple words, economics is an academic attempt to put the world’s limited resources to their best use.