Question

1. She volunteered to help the children.

[Is 'volunteered' a transitive verb or an intransitive verb? In the long man dctionary, I saw "Transitive or Intransitive." What does it mean? Can 'volunteer' be a transitive verb or an intransitive verb?]

From the Longman dictionary:
volunteer2 ●●○ AWL verb 
1 [intransitive, transitive] to offer to do something without expecting any reward, often something that other people do not want to do
volunteer to do something
 Helen volunteered to have Thanksgiving at her house this year.

Answer 1

Yes, some verbs can be both transitive and intransitive, depending on how they're used.

Mostly, "volunteer" is an intransitive verb:

<I>She volunteers at the local homeless shelter.
This Girl Scout troop volunteers at a nearby nursing home, mostly reading to the most elderly patients.
He volunteered to help clean up people's houses after the floods.</i>

Sometimes it's used as a transitive verb, but this is far less frequent:

<I>This teacher volunteered her class to pick up trash on the playground once a week.
</i>