This is partially right. In this case, I would not make “the convenience” the subject. I would say, “New fast food chains have eaten into the customer base of local restaurants” and if you want to mention convenience, you can say “New fast food chains, which are known for their convenience, have eaten…”

Yes, this is a great example. I would just modify it slightly and say, “The sales of online retailers eat into the business of the little local shops.”

Great example .. Social media definitely eats into reading time.

But that’s a great example

Ah great, great example. I think you might want to re-arrange it a little bit and put it in the past tense. You might say, “Not only the pandemic, but also the abundant streaming options have gradually eaten into cinemas’ market share.”

Great … when you use “thereby” you often use an -ing verb after: “Many people are addicted to shopping and spend a lot of money on superfluous things, thereby eating into their savings.”