Gfyuki

The final answer is the name of a fictional character.

Image credits:
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A rearrangement.

The 25 pieces can be rearranged into 4 groups using the coloured circles
as cues, as this crude edit shows.

Where to go from here?

Some partials. Combine with @Weather Vane's answer to put them in the correct order for reading.

If we assume that in the OP they are numbered first row 1-5, second row 6-10, etc., then we have:

1.

THREE = TREE + H

2.

EXISTENTIAL = EXIT + S + VIAL (with V = ENT)
flag of ERITREA

3.

NULL or NULL SET or EMPTY?

5.

? = Silicon + alpha + LA

6.

SEMIJOIN = IMES (reversed) + JOINT - T

7.

? = KA + KATANA + YO (half of YOYO)

8.

SETH, STETH, ? = the letters that fill in the blanks are ETH, and there's an S in a T-shirt

11.

RHO = RHINO - IN

13.

U = capital (Ottawa) ewe

14.

QUANTIFIER = U + ANT + QUID - D + FI + ER (RE reversed)

17.

POUND (453.6 grams is approximately 1 pound)

18.

SCRUPLE = ESC - E + RUBLE (with B = P)

21.

PERPENDICULAR = PEER - E + PEN + DICK - K + URAL (with L and R switched)

22.

TSHE = SETH rearranged to take in order 3142

23.

TACK = TRACK - R

24.

EXCLAMATION = EX + CLAM + AT + ION

25.

DOLLAR = DOLL + AR (god RA upside down)

Solve original image by rows:

Row 1

Three - existential quantifier - braces / empty set - ? - ?

Row 2

right semijoin? - ? - ?eth - ? - vertical bar

Row 3

Rho - Or - Capital lambda - universal quantifier - ?

Row 4

? - pound - scruple - ? - Shang (上)

Row 5

perpendicular - unordered set - ? - exclamation - dollar

Then unscramble the image:

And hazard a guess at the next direction, since everybody else seems to be sharing their partials too:

These are things you get out of your computer, using a couple of keys and plenty of modifier keys. Figuring out the keyboard layout and which keys to use might be useful

Partial answer

Continuing from Weather Vane's observation

that the squares can be rearranged into four groups if we require that the quarter-circles at some of their corners match up,

in fact

those four groups fit in a unique way into the original 5x5 square shape. Some of the rebuses are easier to make sense of than others; so far I have the following:

perpendicular pound empty-set star+ ??doll??

or katakana-yo semijoin ??? ??pilcrow??

rho scruple ??combination-set?? quantifier vertical-bar

seth existential-qualifier capital-lambda exclamation shang

??open-o?? three ??ail?? schwa ??Si-alpha-los-angeles??

which makes me think that

each square is leading to a single symbol, something like this:

⟂£∅??

∨彐⋉?¶

ρ℈??|

?∃Λ!上

ɔ3?Ə?

shoover's answer has some plausible explanations for a few of my gaps, yielding

⟂£∅?$

∨彐⋉?¶

ρ℈Ћ?|

?∃Λ!?

ɔ3⊣Ə?

It isn't entirely clear to me what to do next;

it looks a little as if something good might happen if we read the whole thing upside down, though. (It looks a little like a word-ladder with only one letter changing at each step, but so far I can't make that work.) At any rate it's striking how many upside-down-E-like things there are in the second column. Perhaps the "or" symbol is actually meant to be a vertical bar and we're meant to read the pilcrow, even upside down, as a P, in which case that row yields "pixel". I suspect the open-o may be meant to be read as a D, even though to my mind that only works if we don't invert it. But so far this is all just speculation.