www.instructables.com/id/How-...ainting/ is a yes to your third question.

www.knitpicks.com/content/i...at/dyeing/ includes instructions (under link Gradated Dying Tutorial") for piece dying a small scarf in a stovetop pot

1; always wet the yarn first. it will create a more even color. I would soak the skein carefully with a mild detergent and warm water.
Then taking wet yarn soak 1/2 in dye bath. Slowly raise the dye bath temp from lukewarm to hot, but not boiling. Boiling will felt the wool. You will need an acid for the dye to absorb, vinegar works but I prefer citric acid found in the canning section of your grocer. It's stronger and leave no scent of vinegar and you need much much less.

( never take from hot dye bath into cold rinse water, as this also can felt the wool. take out of hot bath, let cool first before rinsing.)
acid dyes create the most brilliant vibrant colors and do not need to get fixed. Acid dyes are very concentrated, you need much less than procion and direct dyes.

2. for 3 colors, there's a variety of ways.
a) dip 1/3 of yarn in dye bath, repeat for the 2 other colors. ( I take some plastic and cover the already dyed part tying down with rubber-bands.
b) ombre dye: dye yarn from light to dark ..dye yarn in light bath first, then gradually dip less and less of the yarn you end up with a light to dark tone.

Pro-Chemical, Dharma Trading and Aljo Dyes are all on-line and they will mail you instructions on using acid dyes.

for any more dyeing questions, visit the Reconstructed Clothing tribe and see my Dyeing Tips and Tricks posts, there's over 100 posts .

good luck