Learn English – “I’m sorry, I haven’t written (or “haven’t been writing”) to you for a while” – which is better

To your first question:

I have been going on package holidays for years and I have never had any problems.

The Present Perfect Progressive has the meaning of "lately" or "recently." There is no indication from the second phrase that she stopped going on these trips long ago in the past. In fact, it sounds like she still may be taking trips, thus the answer.

The answer to your second question also lies in the second phrase. He is referring to the fact that he was never sick before from the foods he had already tried, not the food he is continuing to try, because obviously the most recent food made him ill.

I have been exploring the world...

The distinction is slight, but perhaps can best be explained as, there is no indication that the subject will stop the activity. The alternative

I have explored the world...

does not hold that implication. It could easily end with

I have explored the world for over 15 years, and it's time for me to settle down.

This is called sequence of tenses.

• I became a zoologist because animals have always fascinated me.

The part "animals have always fascinated me" began in the past and continues into the present. The part "I became a zoologist" occurred at a single occasion in the past.

If you want to say that "animals fascinated you" in the past but not any more you need to use the Past Perfect tense:

• I became a zoologist because animals had always fascinated me. - This whole sentence is about the past.

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