Learn English – A tag question with third conditional

For the first example, isn't it is correct. Don't we does not make sense in this context. The sentence should be:

It's very important that we eat healthy food, isn't it?

The second example, I would not use either option. Instead, I would use isn't it here as well:

It's a must that all applicants follow the rules of the competition, isn't it?

The reasoning for this is that it coincides with the beginning of the sentence. For example, I might use any of these:

They should eat healthy food, shouldn't they?

There are a lot of people here, aren't there?

You are connected to the Internet, aren't you?

Don't and didn't are exceptions to this:

You have an Internet connection, don't you?

He came to work yesterday, didn't he?

One should study hard, shouldn't one? One can be used as a subject of question tag because it is a personal pronoun and can refer to the subject one.

One should do one's duty.