Is it permissible to read part of the verse "Do not kill the soul that Allah has forbidden except by right" to teach children without seeking refuge (from Satan)?

There is no harm in reciting part of a verse for the purpose of teaching and referencing, provided there is no change in meaning. Scholars have explicitly stated the permissibility of reciting part of a verse in prayer, and that it fulfills the Sunnah. If it is permissible in prayer, then teaching is even more deserving of permissibility.

As for seeking refuge (reciting isti'adha) when intending to recite the Quran, it is recommended according to the majority, and not obligatory. There is no need for isti'adha merely for mentioning a verse or part of it for teaching purposes, as the context is not one of recitation. Al-Suyuti mentioned that the correct approach is to say "Allah Almighty said," and then mention the verse, without isti'adha.