"I like dogs better than cats."
"I like a dog better than a cat."
The difference is very subtle. In the first sentence we are talking about dogs and cats in general, while in the second sentence we are talking about any dog and any cat that exists. In this case, we would usually use the first sentence, although the second is not wrong. But consider this:
"If we decide to have a pet, I'd like a dog better than a cat."
Here, we're definitely talking only about one animal -- either one dog, or one cat. It doesn't matter which dog or which cat, the speaker would prefer to have a dog -- only one.
"We saw deer in our backyard. The deer was nipping the branches."
"Deer" here is actually a plural, so the second half of the sentence makes more sense as "the deer were...". In this case, since we're not talking about deer in general -- just a small subset of deer -- we would also say "We saw some deer...", although it's not incorrect without "some". Many grammar books treat "some" as the plural of "a", and that's actually quite helpful.
As for your sentences:
1. Yes, very good.
2. You
can say "A supermarket..." in certain circumstances, but you're really talking about supermarkets in general, so "Supermarkets are..." sounds better.
3. Yes, that's correct.
kimroen, the most important reason for not using articles is when we are talking about things in general. For example:
I saw a cat.
That's one specific cat. I don't know the identity of the cat, but it was a specific cat.
I like cats.
That's cats in general. It doesn't matter which cat it is, I like them all.