A word that conveys that an act or expression or object had failed to fulfill its purpose

I'd say

• "The donation made in vain was never meant to be made in good faith.".

In the second sentence "neglected" seems to fit the case.

• The neglected apology implies a lack of actual remorse on the part of the directors of the board.

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Addition due to a comment from user Rahul Ahuja

1.

(OALD) (idiom) without success (Topics "difficulty and failure")

(What is not successful is a failure and vice versa.)

2.

The only description in this second query is that there is an intention to make an apology but this is not done. more than that can't be inferred. The term sought must remain then within the bounds of this specification; of course, one may be more precise.

What you're asking for is a way of saying that even though something is normally meant in a certain way, somebody is simply going through the motions in a kind of insincere fashion. They're not really concerned with the normal result of the action, but are doing it for the sake of appearances only.

An idiom that expressed this is for show:

[Merriam-Webster]
1 : intended to be seen but not used or bought
// We're not supposed to eat the fruit on the table. It's just for show.
2 disapproving : done in order to gain the approval or favor of others
// He says he enjoys classical music, but it's only for show.

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An actual adjective that fits the example sentences is perfunctory:

[Merriam-Webster]
1 : characterized by routine or superficiality : MECHANICAL
// a perfunctory smile
2 : lacking in interest or enthusiasm

So:

The perfunctory donation was never meant to be made in good faith.
The perfunctory apology implies a lack of actual remorse on the directors of the board.

If the effort was not intended to be effective, I'd call it bogus:

Not genuine or true; fake.

If an effort "fell flat", presumably without intent, it's often referred to as a dud:

A thing that fails to work properly or is otherwise unsatisfactory or worthless.

Ineffective fits both the question title and the example sentences.
The ineffective donation ...
The ineffective apology ...

“The grandiose donation was never meant to be made in good faith."

“The duplicitous apology implies a lack of actual remorse on the directors of the board."

grandiose: Donation implies magnanimity.

From M-W dictionary: grandiose: impressive because of uncommon largeness, scope, effect, or grandeur.

duplicitous: because you use the word hoodwinked in your question.

"The so-called donation was never meant to be made in good faith."

"The so-called apology implies a lack of actual remorse on the directors of the board."

OED

So called (adj.) 2. In attributive use (hyphenated): Called or designated by this name or term, but not properly entitled to it or correctly described by it. Also loosely or catachrestically as a term of abuse.

1884 A. R. Pennington Wiclif vi. 193 Their so-called poverty is nothing else but a diabolical lie.

1980 W. Safire in N.Y. Times Mag. 13 Jan. 6/1 Examples of sneer words are ‘self-proclaimed’, ‘would-be’, ‘purported’ and that Soviet favorite, ‘so-called’.

Note the 1980 quote also gives you alternatives.