Hardly, hardly ever, hardly any

I've learned that the words hardly and rarely have the same meaning and that moreover we can use these words interchangeably in any sentence. Is this right or wrong?

They are not quite interchangeable as they stand, but need some modification first of all. If we add ever to hardly to arrive at hardly ever, then this is synonymous with rarely and also with seldom.

hardly ever

These adverbs describe how frequently or regularly something happens. Thus along a spectrum of frequency, starting with most frequent and ending with least frequent, we might find the following:

• Well doctor…. I always have two meat rolls for breakfast. Without fail. Every day.
• I usually have poached eggs on toast at the weekend. Not every weekend. But most weekends.
• I often / frequently have two chocolate biscuits or a pastry with my morning coffee. Not every day. But most days, I have to confess.
• And I sometimes have a brandy with my coffee after
  lunch. After a particularly good lunch.
• I hardly ever / rarely / seldom eat a full English
  breakfast. Once every two months perhaps.
• I never drink coffee after 7 p.m. Always tea. So what do you think is causing the high blood pressure?

Note that hardly ever, rarely and seldom equate with occasionally or very occasionally in terms of frequency, but that when you use hardly ever, etc, you are putting a negative gloss on what you are saying. Occasionally sounds much more positive. Compare the following:

• I occasionally see my daughter when I'm up in London. If she's free, around lunchtime.
• I hardly ever see my daughter. She's far too busy to find time for me.

hardly

Hardly, as an adverb by itself, means only just, and equates with barely and scarcely.

• Jonathan could hardly walk but already knew how to swim.
• I barely / hardly / scarcely knew Jack, although I know he was a great friend of John's.
• We had barely / hardly / scarcely finished dinner when they arrived.

hardly + any (+ -one/-thing)

Hardly any means very little or very few and is the opposite of plenty of, or colloquially, loads of. Note again the negative tone in which it is used:

• I've got plenty of friends, but hardly any money.
• I knew hardly anybody at the party, but Katie knew loads of people, nearly everybody in fact.
• It's worth hardly anything - practically nothing! Just a few pounds, perhaps.
• He's hardly said anything to anybody since the accident.
• He's said hardly anything to anybody since the accident.