You should only get as many cards as you declare - three
The character being removed from the deck's presence opens up some some cause and effect chains, but it is the two remaining cards (not yet drawn) that erupt after the hour, not "the whole deck unleashes at once" as stated in the question's text.
Three cards should get drawn, but the last two may not be usable
If you fail to draw the chosen number, the remaining number of cards
fly from the deck on their own and take effect all at once.
If you declare three, and you only draw one, then after an hour the other two cards come out of the deck and take effect immediately. The text does not specifically state "the whole deck," so this reading of that description makes the most sense to me.
That doesn't completely solve the conundrum. The DM will need to make a ruling on which card takes effect first, but the description suggests that you aren't drawing the cards at this point: they are being drawn for you by the magic of the deck. Let's call that "autodraw."
The above 'draw no more cards' lacks a card drawing character, but it leads to some other "how does this work?" questions for the DM to resolve.
Example based on your scenario:
First card: Jester (yay, XP for you)
Fail to draw, so one hour later ...
Second Card (autodraw): Donjon (you are trapped!)
Third Card (autodraw): The Fates (you can undo Donjon1, lucky you)
or
Third Card: Balance (you are trapped and you change alignment).
or
Third Card: Knight (The DM may rule that he appears wherever you are trapped, so maybe he can help you get out1, but he may appear where the deck is and where you are not).
1 What suspended animation means, for this result, isn't explicitly spelled out
Donjon. You disappear and become entombed in a state of suspended
animation in an extra-dimensional sphere.
We can get an idea from the Astral Projection spell description (PHB, p. 215):
... the material body you leave behind is unconscious and in a state of
suspended animation; it doesn’t need food or air and doesn’t age.
The Sequester spell description (PHB, p. 74) says for suspended animation ...
"Time ceases to flow for it{what's being protected by the spell} and it doesn't grow older."
It appears that you'd be awake, and maybe able to communicate with that Knight, but the DM may rule otherwise. (For example, the DM may rule that the Knight pops into existence where you are as you pop into that other place).
Which spell description's sense applies? DM ruling needed here.
There is no further autodraw
This is a textbook example of the Specific vs General rule that D&D is built on.
The general rule for the deck is that the deck draws for you if you cannot/do not complete your declared draw.
The specific rule given by Donjon and the Void cards modifies this rule to alter what occurs (namely that you do not draw any more cards).
The Fool has a similar specific rule which increases your card draw by one.
Best Answer
As the deck notes.
If you don't name a number then any cards you draw will be in excess of that and have no effect.
The rules as you note also state.
So, if you want to trigger the magical effect, you need to declare a number.
Exactly what happens if you try to draw a card before you declare a number isn't stated. Maybe it doesn't work, stopped by powerful magic. Maybe nothing happens. It depends on the whims of the DM and the artifact.