Do I need council permission to remove a tree?
Sometimes. Protected and notable trees, and trees in some zones or near waterways, need consent, and the rules differ by council. An arborist working in your area will know, and can write the report if one is required.
What about a tree near power lines?
That is specialist work with legal minimum approach distances, and in some cases the lines company does it or has to disconnect first. Say power lines are involved in your request and only qualified people are asked.
Is the arborist insured?
Ask, and ask for the amount. This is the trade where it matters most: the worst case is a limb through a roof, and you want that covered by their policy rather than yours.
Is stump removal included?
Usually quoted separately, because it needs a different machine. Say whether you want the stump gone or just ground down, since that changes the price and the access needed.