Is sequence and immediate succession a condition for the words of the Adhan, and is ritual purity a condition for the Adhan?

Order is a condition for the adhan. If the muezzin utters some phrases of the adhan and puts what should be delayed ahead, or vice versa, what he put ahead or delayed becomes invalid. He should then build upon what he uttered in the correct order. It is preferable to restart the entire adhan so that it is continuous.

Purity is not a condition for the validity of the adhan, but it is recommended. So, if a person in a state of minor impurity (muhdith) or major impurity (junub) gives the adhan, it is valid, but it is disliked.