Facebook is showing others my latest new added friends, saying something like "Aiwnas is now friends with X." Is it possible to stop Facebook from doing this? Or make it private for a customized list of my friends?
The only way to stop facebook notifying your friends of your friendship changes is to make your friends list private. Go to your friends list page. At the top right section of the page click on Edit button. There you can choose who can see list of your friends (only me, custom, friends, everyone). Whoever can see list of your friends can find out whom you just became friends with.
So if you need to hide friendship notifications from some of your friends you need to make a custom list.