The Top Ten Elements You Won't BELIEVE Are In This Array

Jelly, 142 bytes

I>-ṣ0ṖS€ỊÐḟ‘ɓĠL€ḟ1,ɓ¹ƝÆPẠ$ÐfW;ɓLẋ<¥21W;ż@€"“æƥu®ụ³Km&|°ẓz“ṿ$¥{d3ɓFȤSJẎVḍnṃ*¹0Ḟ¬ȤɲƝċƲạB'ɼɓ.€⁺Ƒ“¢ßUṡʠx\~⁻ḅėʠAƓḳ¶e<“½ė!Ƙ¥Ḍ3]⁷ṀƭȮþċ⁽?ṫĠƁÆȦØ⁾Ż»ṣ€⁷¤

A monadic link accepting a list of integers, returning a list of lists of clickbaits (each of which is a list of characters and integers). For a full program printing line-feed separated clickbaits just add ẎY to the end.

Try it online! (Footer makes a single list of clickbaits and then separates them with new-lines.)
...or see the example given in the question.

How?

The 99 right-most bytes of this Link form a nilad (a function with zero arguments, i.e. a constant):

“...“...“...“...»ṣ€⁷¤
                    ¤ - nilad followed by link(s) as a nilad:
“...“...“...“...»     - list of compressed strings (the four clickbait-texts with the
                      -   integers replaced with line-feed characters)
                   ⁷  - literal line-feed character
                 ṣ€   - split-at for €ach (read to interweave with the integers)

Let's label these text-parts as X, now the Link is:

I>-ṣ0ṖS€ỊÐḟ‘ɓĠL€ḟ1,ɓ¹ƝÆPẠ$ÐfW;ɓLẋ<¥21W;ż@€"X - Link: list of integers Z
                                             - # get the monotonically increasing runs:
I                                            - incremental differences of Z
 >-                                          - greater than -1 (vectorises)
   ṣ0                                        - split at zeros
     Ṗ                                       - pop (discard final run)
      S€                                     - sum each (length - 1 for all runs)
         Ðḟ                                  - filter discard if:
        Ị                                    -   insignificant (discard any 0s or 1s)
           ‘                                 - increment (yielding all run-lengths >= 3)
            ɓ                                - new dyadic chain with that on the right
                                             - # get the multiplicities:
             Ġ                               - group indices of Z by value
              L€                             - length of €ach
                ḟ1                           - filter discard 1s
                  ,                          - pair with right (the run-lengths)
                   ɓ                         - new dyadic chain with that on the right
                                             - # get the prime-pairs
                     Ɲ                       - for each pair in Z
                    ¹                        -   identity (do nothing)
                          Ðf                 - filter keep if:
                         $                   -   last two links as a monad:
                      ÆP                     -     is prime? (vectorises)
                        Ạ                    -     all?
                            W                - wrap in a list
                             ;               - concatenate with right ([multiplicities,runs])
                              ɓ              - new dyadic chain with that on the right
                                             - # get top count as a list
                               L             - length
                                   21        - literal 21
                                  ¥          - last two links as a dyad
                                 <           -   less than? (1 if 20 or less, else 0)
                                ẋ            -   repeat ([length] if 20 or less, else [])
                                     W       - wrap in a list (i.e. [[length]] or [[]])
                                      ;      - concatenate with right ([[prime pairs],[multiplicities],[run-lengths]])
                                             - ...now we have [[length],[prime pairs],[multiplicities],[run-lengths]]
                                          "X - zip with X (the text-parts)
                                         €   -   for each (item in the current list):
                                       ż@    -     interleave with swapped arguments

Java 10, 467 457 456 453 bytes

a->{int l=a.length,i=0,p=0,P=0,m[]=new int[999],t;String e=" Elements ",r=l<21?"The Top "+l+" Array"+e+"\n":"";for(;i<l;r+=i>0&&p(p)>1&p(t=a[i-1])>1?p+" And "+t+" Were Spotted Together, You Won't Believe What They Did\n":"",m[a[i++]]++)if(p<(p=a[i]))P++;else{r+=P>2?P+e+"Sort Themselves, Find Out What Comes Next\n":"";P=1;}for(;l-->0;r+=m[l]>1?"These "+m[l]+e+"Will Blow Your Mind\n":"");return r;}int p(int n){for(int i=2;i<n;n=n%i++<1?0:n);return n;}

Assumes the input-array will contain values 0 < N < 1000 ([1,999]).

Try it online.

a->{                     // Method with integer-array parameter and String return-type
  int l=a.length,        //  Length of the input-array
      i=0,               //  Index-integer
      p=0,               //  Previous item, starting at 0
      P=0,               //  Sequence-counter, starting at 0
      m[]=new int[999],  //  Element-counter array, starting filled with 0s
      t;                 //  Temp-integer to reduce the byte-count
  String e=" Elements ", //  Temp-String " Elements " to reduce byte-count
         r=l<21?         //  If the size of the input-array is 20 or less:
            "The Top "+l+" Array"+e+"\n"
                         //    Start the result-String with 'length' gossip-line
           :             //   Else:
            "";          //    Start the result-String empty
  for(;i<l               //  Loop over the input-array
      ;                  //    After every iteration:
       r+=i>0&&          //     If this is not the first item,
           p(p)>1&p(t=a[i-1])>1?
                         //     and the current and previous items are both primes:
             p+" And "+t+" Were Spotted Together, You Won't Believe What They Did\n":"",
                         //      Append the 'two primes' gossip-line
       m[a[i++]]++)      //     Increase the counter of the current value by 1
    if(p<(p=a[i])        //   If the previous item is smaller than the current:
      P++;               //    Increase the sequence-counter by 1
    else{                //   Else:
      r+=P>2             //    If the sequence-counter is 3 or larger:
          P+e+"Sort Themselves, Find Out What Comes Next\n":"";
                         //     Append the 'sequence' gossip-line
      P=1;}              //    Reset the sequence-counter to 1
  for(;l-->0;            //  Loop over the Element-counter array
      r+=m[l]>1?         //   If this element occurred at least two times:
          "These "+m[l]+e+"Will Blow Your Mind\n":"");
                         //    Append the 'occurrence' gossip-line
  return r;}             //  Return the result

// Separated method to check if the given number is a prime
// If `n` is a prime, it remains the same; if not: either 1 or 0 is returned
int p(int n){for(int i=2;i<n;n=n%i++<1?0:n);return n;}