I can answer those.
Livingston: Rest. Like you said, he has played a ton of minutes this year and his first heavy minutes season since that horrific injury. Amazing what he has done to get back to playing again.
Gutierrez: Took Livingstons minutes. He saw some minutes the last few weeks as he was only signed recently so my guess is they were seeing what he can do. 3rd string PG, 12th in rotation.
Teletovic: Doesn't always play the right way. Sometimes the matchups don't favor him. He isn't a great defender, slowish, and takes suspect shots from 3 even though he is a great shooter. He will take shots just to get his shot numbers in, even if a defender is closing on him. Plumlee may take his minutes in the playoffs and push Blatche back to PF. Depends on matchups, heck he played some center against the Heat last game.
I say it now, look out for Brooklyn, if they get to Indiana in the second round an upset is brewing. These guys are deep, and playoff built even without Lopez.