Question 1

How many tiny copper wires are there inside of one singe jumper wire?

Accepted Answer

in total 10 tiny copper wires inside of single jumper wire

Question 2

Can these work on a raspberry pi breadboard?

Accepted Answer

They will work with anything that has either male or female dupont pins for connection to external devices. The cables with male ends can be soldered too.
Short answer: yes.

Question 3

can these be used on ATX mother boards for pc, as a power switch extender?

Accepted Answer

No, these cables are well suited to low voltage and fairly low current.  They are ideal for data and power delivery of 3.3v - 12v in prototyping (breadboard, GPIO type) applications, but both the wire (usually around AWG24) and the pins are rated for <5 watts (so 5 volts at 1 amp for example) .  They are also not shielded in any way.  
The average ATX type PC power supply  puts out tens of amps at the 3V3, 5V and 12V rails, which is many times more than this gauge of cable can handle; compared to this cable at AWG24, most PC power supplies use cables rated AWG14-AWG18.  There are many ATX extension cables for exactly the purpose you're looking for but these Dupont cables are most definitely not good for that use case.  
As to the other answer from "ur", I most definitely would NOT try passing 220V through this type of cable.  The effects would be catastrophic - 220V @ 1A = 220W on a cable with a maximum rating of 5W = melted cable, probable damage to power supply and computer and likely a small fire to go along with it.

ASIN	B07SYKPB86
Best Sellers Rank	62,303 in Business, Industry & Science ( See Top 100 in Business, Industry & Science ) 75 in Jumper Wires
Brand	Yizerel
Colour	Multi-coloured
Customer Reviews	4.6 4.6 out of 5 stars (174)
Item Highlight	To Female x 3, 40 Pin Male x 3, Female x 3, Breadboard Jumper Wires Ribbon Cables Kit (360 Wires)
Manufacturer	Yizerel
Manufacturer Part Number	DB-XX-ZH
Material	Aluminium, Copper
Model Number	DB-XX-ZH
Number of Items	360
Strands	Single Strand
UPC	741663639526
Unit Count	360.0 count

360 Pcs Multicolored Dupont Wire 40 Pin Male, Ribbon Cables Kit for Arduino

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