Wire nuts if you keep twisting hard will twist the wires without that extra step.
Yes, but it takes a little extra skill to get them all lined up nice and parallel first, so they twist evenly.
This is how I usually do it, but there is one important step here. If a wire somehow slipped behind the others, it may not end up twisted with the rest of the pack. Once you have it nice and tight, give a good tug on each individual wire, to be sure they're all together, if you choose to do it this way.
If your combining stranded with solid wire, it helps to "lead" the stranded wire slightly. Especially if your joining one solid with one stranded. This keeps the stranded conductor from just wrapping around the solid conductor and not being gripped by the wire connector.
THIS is great advice! You cannot pre-twist a solid and stranded mix. The more flexible stranded will just wrap circles around the solid. The point of twisting is to get both wires to coil around each other, so they lock together.
One other piece of advice. Be very careful how you strip the wires. Put a nick where you strip a solid wire, and the whole end may want to break off. Do this in stranded, and you lose strands.
Seriously, some of the wires in my house are soldered and taped. Not a wire nut to be found. Apparently they did things differently in the 20's. That was on BX type cable.
In my house, I have cloth insulated BX with soldered connections. They twisted, soldered, and then held it together with a solid ceramic wire nut. It isn't bad if you don't plan on messing with it, but open it up, and things become a nightmare to work with.