I tried using ARRAYFORMULA using whole columns (e.g. A:A, B:B, etc.) but if it's a formula where I need a result output to each row

you can always freeze it like:

=INDIRECT("A:A")

this way you can add rows anywhere you want (if you of course not add new row above the row that holds the formula - that would be troublesome to fit in A:A into A2:A)

that the INDEX function just does not work with ARRAYFORMULA at all

INDEX is already ARRAYFORMULA type of formula. the analogy being here as: you need a car to get from A to B where INDEX is a blue car with 3 doors and ARRAYFORMULA is a red car with 5 doors - it doesn't matter what color you have, you just need a car

= IF (G2 <> G1, 0, B1 + 1)

while this is direct logic there are several ways how to achieve the same thing. proper usage would require not to use such formulas as ARRAYFORMULA in column G or B to avoid circular dependency errors. for a simple resetting count up try:

=ARRAYFORMULA(COUNTIFS(B1:B7, B1:B7, 
 SEQUENCE(ROWS(B1:B7)),"<="&SEQUENCE(ROWS(B1:B7))))

feel free to change B1:B7 to open range or frozen range...

update:

=INDEX(IF(B2:B="";; COUNTIFS(B2:B; B2:B; 
 SEQUENCE(ROWS(B2:B)); "<="&SEQUENCE(ROWS(B2:B)))-1))