Hi,
These sentences mostly sound natural in everyday spoken English. Here’s a quick check:
His cooking skills have improved a lot over the years.
Natural and common.
Over time, bad habits can become so deeply ingrained that they are very difficult to break.
Correct and natural.
Over time, bad habits can become so deeply ingrained that it's very difficult to break them.
Also fine and slightly more conversational than sentence 2.
Online scamming has gotten more and more sophisticated over the years.
Natural. "Gotten" is American English. In British English, use "has become."
His passion for literature only grew stronger over the years.
Natural and clear.
We haven't stopped laughing since the show started. It's a sure thing.
First sentence is fine. The second ("It's a sure thing") sounds odd here. You could say:
"It’s been a hit" or "It’s definitely funny" instead.
He hasn’t stopped complaining about the new manager since day one.
Natural and common in speech.
I’ve been getting nonstop spam calls over the past few days.
Sounds natural and casual.
The prices of basic goods have kept going up over the past few years.
Correct, though more natural:
"Prices of basic goods have kept rising..."
The prices of basic goods haven’t stopped rising over the past few years.
Natural and idiomatic.