You have two options:
1. Cut the wool every time you change colour, this will leave you with a little pink tail hanging off after you do a pink section, and you would weave in the ends on the pink section of the knitting, same for the black.
This means you will have to weave in two tails for each stripe - fiddly, boring, and tedious.
- When you finish a pink stripe, put down the pink wool. Grab the black wool from the previous stripe which was not cut off, it was left dangling from the start of the pink/end of the black stripe, start knitting with the black for the new stripe. This is easier, but the finished scarf will have a strand of black going vertically up the side of the pink stripes (going along the long edge), and vv. for the black stripes. This is called carrying your wool up the side of the work.
If you choose this option, you can weave the black into the pink stitches on the way up the side, so it will not form a loop that can be pulled away from the knitting, but this will be just as visible, and slightly more messy-looking.
However, I would do something called a Russian join. http://www.geocities.com/mama_bear_007/Russian_Join.html
This means no ends to weave in (except the start and end), no knots, no black bits in the pink bits (ooooh!), I highly recommend it. Don't be put off if the directions looks a bit confusing, sit yourself down in front of the computer with a sharp needle and practise on 2 strands a foot long each, you'll get the idea.
Do be sure to place the colour change right where you want the stripes to change.
Well, that's a third option, but you may be entirely happy to carry up the side.
I always do a plain cast-off even for seed or moss stitch and don't have any problems that way. For size, can he try it on, or is it a surprise?
Are you asking because you don't know what's a good size for his height, or you don't know what size he prefers?
If it's a secret present: For his height, I would go ask someone of similar size to put it on to help you decide. For his preference, look in his cupboard for any other scarves he has, and see how wide they are.
Generally for a man, I'd go with 14-18 cm wide, but that's personal taste. However I do think a narrower scarf is more feminine and most men prefer wider. Considering the scarf already has pink in it, and he's a big guy, I would do about 16-20 cm wide, but remember this is down to your and his taste.