How often should the lawn be mowed?
Weekly to fortnightly through spring and summer, and monthly or less over winter. Most people book fortnightly year round and let the gardener skip the quiet months.
Who takes the green waste away?
Sometimes the gardener, sometimes you. It is the most common thing that makes two quotes look different, so ask for it to be stated either way.
Do I need an arborist instead?
For anything large, near power lines, or needing a chainsaw at height, yes. Say what the tree is and roughly how tall in your request, and the replies will tell you which trade it needs.
Can someone maintain the garden while I am away?
Yes, and it is a common request over the holidays. Agree access and watering in writing before you go rather than by text from the airport.