Need clarification about wiring - newbie

(deleted)

When you want the connection to be reliable and (mostly)permanent.

A "jumper wire" can mean either any short piece of wire or conductive material used to connect two points. (the little black rectangular things used to connect two adjacent pins in 0.1 header are called jumpers, and in casual usage, 0 ohm resistors are also sometimes referred to as jumpers). However it often refers to specifically wire meant for hobby/prototyping, sold in short lengths equipped with pins on either end to connect to pin header.

Yes, male 0.1" dupont* jumper wire is perfect for plugging into female headers or breadboards. Female dupont jumpers are great for connecting to male headers (and do a better job, all else being equal, than male jumpers going into female header)

*DuPont's name is associated with the common 0.1" connectors used with pin header, presumably because they originally made that series of connectors.