どうもありがとう, Sakura-san. It is always very good to read posts like these from our Japanese fellows.

In the first case, "Please let Nazuna kill Colibris" is a perfectly clear phrase in English. It is polite, and clear. If you wish to give more detail, "Please let Nazuna get killshot for Magian Trial" is also an acceptable phrase.

In the second case, "Take turn, please?" is easily understandable and polite. If you wish for an ideal phrase, "May we take turns?" also works well.

Your English is very good, and very polite. You do not have to worry about being rude . がんばってください!