Tukukkk

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)

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 right-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??

(Credit to Bass for noticing that it's specifically a right semijoin, which I hadn't spotted.)

I haven't given detailed explanations of how the rebuses work because I think they're mostly easy to see once you have the answer, but here are a couple of the subtler ones:

"schwa" is because we have the German flag, we're pointing to its black stripe, hence schwarz (German for black), and we want 5/7 of this, making schwa. "katakana yo" is because "ka" has been inserted into the middle of a katana (plus half a yo-yo). "or" is half an Afro, reversed. I don't actually believe "seth" since it doesn't seem to be the name of a symbol, but the point is that you can insert "eth" into all those gaps. "Shang" is because we have a picture of some towers in Shanghai, plus a gap followed by the "hai" character.

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!上

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 and I think it's probably wrong.) 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. It's possible that the fourth row might say "fiver", in which case maybe I can pretend that the second row says "hazel" and there's a Watership Down reference going on. But so far this is all just speculation.

Ah!

I bet it says DETECTIVE - LIVED BAKER STREET, in which case the answer is SHERLOCK HOLMES. (Credit where due: this did not occur to me until I saw Bass's inspired guess that in the mysterious Los Angeles box "Si" is a typo for "Sn", so that that square contains an "a".) If this is right, then clearly I have entirely the wrong symbol in the middle of the first line (an empty set) since it looks nothing like "re" or "ee".

Solve original image by rows:

Row 1

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

Row 2

right semijoin? - katakana yo - small eth - schwa - vertical bar

Row 3

Rho - Or - Capital lambda - universal quantifier - pilcrow

Row 4

open o - pound - scruple - ? - Shang (上)

Row 5

perpendicular - unordered set - tie? - 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 all are unicode characters of some kind. Particularly of the kind that look like upside-down letters. Write them down, stand on your head, and read.

Like so: (to be finished soon)

 ⟂ £ ∅   $

 ∨ ヨ    ¶ 

 ρ ℈   ∀ |

 ð ∃ Λ ! 上

 ɔ 3 ꄟ ə Ɑ