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https://en.wikipedia.org/wiki/Western_Union_splice

Flux+touch: strip a relatively long length of both wires. Twist them together in a way so that the whole thing remains in a line. Touch with flux. Touch iron tip to solder. Touch soldered tip to wires. (Flux will flow through) Heat shrink after. (You may need to place the heat shrink first)

Yes. My workflow usually includes:

5) scream obscenities because you forgot to thread the heat shrink tubing before soldering.

6) snip wires

7) goto step 1

You mean something like this? https://www.adafruit.com/product/3786

Stranded wire to stranded wire, or solid wire to solid wire? Or mixing stranded and solid? Same gauge or mixed gauge?

All of them, as in practice you'll encounter them all sooner or later.

Err don’t!