Learn English – Present Perfect and Past Progressive with wait

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.

1. The website you link does not say that “Often we use “Non-progressive ... ” but that “we use stative verbs in this situation”. Stative and non-progressive are two different things.

   • Non-progressive means ‘not cast in the progressive construction’; a more usual term is simple (‘simple present’, ‘simple past’). The ‘progressive construction’ is that which employs a form of the verb be followed by a verb in the -ing form. None of your sentences employs the progressive construction; all are non-progressive. Progressive versions would be these:

     1a. ^? I have been knowing John for years.
     2a. ^∗ I’ve been being there since 2011.
     3a. ^okI’ve been living here since 2011.
     4a. ^okI’ve been smoking since I left school.

     Note that 1a is marked as ^? marginally acceptable and 2a as ^∗ unacceptable. More about that in a minute.

   • A stative verb is one which expresses a state rather than an event; know and be are statives. Other sorts of verbs, those which express events rather than states, are called eventive (or sometimes dynamic); live and smoke are eventives. Live is of the type of eventive called activity verbs: these are similar to statives in that they have duration in time and do not have a goal or endpoint ‘built in’ to their senses. Smoke when it is used intransitively (John smokes) is also an activity verb; but when it is transitively (John smoked a cigarette) it is an achievement verb, one which has both duration and an endpoint (the endpoint is when John finishes the cigarette).

     One important distinction between statives and eventives is that statives are not ordinarily cast in the progressive construction. (This is apparently because the progressive construction is typically employed to ‘recategorize’ verbs of any type as current states, and statives are, of course, stative already!) For instance, we do not say

     ^∗ I am knowing algebra.
     ^∗ I am being a student at the University.

     In the last generation or so this rule has been increasingly relaxed in some contexts, especially in conversation, and it may eventually disappear. Be, however, is a special case. When you cast be in the progressive it takes on a different meaning: it turns into an activity verb meaning behave.

     John is being a jerk = John is behaving like a jerk.
     John is being foolish = John is behaving foolishly.

2. The perfect construction is inherently ambiguous. What it ‘means’ is that the past event or state it mentions gives rise to some present state; but what that state is is left to the hearer to figure out, which may involve looking at not just the rest of the sentence but the surrounding discourse as well.

   In particular, perfects like I have lived in Paris since 2002 may have either a continuative meaning (I started living here in 2002 and I am still living here) or an experiential meaning (I lived here for a while at some point in the past after 2002).

   One strategy for avoiding this ambiguity is to cast a perfect into the progressive construction when it is intended to bear a continuative sense: I have been living in Paris since 2002 can only mean that I have lived there right up to the present. And this strategy is extended more and more frequently to stative verbs, exerting a force contrary to the rule against casting statives in the progressive. That is why I have been knowing John for years is now moving toward acceptability: it makes it wholly unambiguous that I still know John today.

This whole issue is discussed in stupefying (but nonetheless inadequate) detail at our Canonical post What is the perfect, and how should I use it?, especially §§ 3.1 Grammatical meaning and 3.2 Pragmatic meaning.