Countif without CSE, unpredictable behavior

[crazykvex]

I've stumbled upon a feature of Excel which I do not understand. In the table below I've tried to strip down my issue to its bare essence:

X	COUNTIF(A1,A3:A4) evaluates to: 0	F9: {1,0} evaluates to: 1	INDEX(COUNTIF(A1,A3:A4),1,1) evaluates to: 1
	COUNTIF(A1,A3:A4) evaluates to: 0	F9: {1,0} evaluates to: 1	INDEX(COUNTIF(A1,A3:A4),1,1) evaluates to: 1
X	COUNTIF(A1,A3:A4) evaluates to: 1	F9: {1,0} evaluates to: 1	INDEX(COUNTIF(A1,A3:A4),1,1) evaluates to: 1
Y	COUNTIF(A1,A3:A4) evaluates to: 0	F9: {1,0} evaluates to: 1	INDEX(COUNTIF(A1,A3:A4),1,1) evaluates to: 1

In the second column, COUNTIF is used to find the values in cells A3:A4 in cell A1 (NOT as an array formula, so no CSE).
The result puzzled me: it was zero, unless the formula is entered on the third line (the same line containing the match).

My main question is

Main Question: what is Excel's evaluation sequence of COUNTIF(A1,A3:A4) and why does it lead to different results based on the row in which the formula is entered?

I also noticed that if I evaluate the formula of each cell separately using F9, the answer is always {1,0}, and after hitting ENTER, the answer is always 1

Bonus Question 1: How can evaluating an equation using F9 change the result?

When the formula is surrounded by INDEX(...,1,1) the problem is solved, a method I stole from Aladin

Bonus Question 2: How does Aladin's workaround solve the row-depencence problem?

Can somebody help me with my (preferably the main!) question?

 

[crazykvex]

Small change on the first post: the INDEX(...,1,1) formulas should be INDEX(...,0,0). Unfortunately I am not allowed to change this in the post itself, that's why I post it separately. Sorry for the confusion.