'let down'

  1. They have the feeling of let down by their elected representative.
  2. They are feeling of let down by their elected representative.
  3. They are feeling let down by their elected representative.
    Are they all correct?
    Thanks.
  1. They have the feeling of being let down by their elected representative.
  2. Incorrect. Use 3.
  3. They are feeling let down by their elected representative.

Usually:
They feel that they have been let down by their elected representative.

Beeesneees,

  1. They are feeling let down by their elected representative.
  2. The residents are feeling squeezed by rising service charges.
    IF “squeezed” is a past participle or an adjective, what is ‘let down’?
    Please explain the grammar involved in this sentence?
    Thanks.

oald8.oxfordlearnersdictionaries … y/let+down

Beeesneees,
Oxford defines ‘let-down’ as a noun.
Can I say?:

  1. They are feeling let-down.
  2. They are feeling fever.
  3. They are feeling temperature.
    Please explain the grammar points to understand well.
    Thanks.

Different words, different contexts.
You can say ‘they are feeling feverish’ and ‘they are feeling hot’.
Once again: you cannot effectively define rules by matching phrases and types of words in the way you try to do.