Learn English – “What is the point” or “What is the purpose”

This may be idiomatic or specific to American English, in which case it might not apply to the news you're seeing. But I would almost always use "refurbish" for a piece of furniture or equipment - something moveable. I would use "renovate" exclusively with a building or structure.

I would buy a recently refurbished laptop or couch.

I would buy a recently renovated house or apartment.

I don't think it's wrong to say the apartment has been refurbished; it's probably technically correct, but it sounds off to my ear.

They are definitely related words, and your sentence could probably work with either of them.

To put the three in order from broadest to most specific: motivation, purpose, objective.

Motivation often refers to an internal/emotional drive, or general goal

Purpose can refer to a general drive, but usually refers to something more concrete

Objective usually means a specific goal.

In an example: My motivation for joining running club is that I want to be healthier, my purpose is to increase my running stamina, and my objective is to complete a marathon.