Question

Can a public question at full council be minuted?

Answer 1

The minutes of a council meeting are a record of what council business was discussed and what actions were agreed.   Yes, a specific public question can be minuted verbatim , but that doesn't mean to say it must be. The question need not be quoted verbatim either and the response might not be quoted in any detail.  For example A Council might have in its minutes  "Public Participation"  A resident asked for the dates the Parish Council cut the grass on the village greens.  The Clerk responded with the information requested."  Another minute from another council could say "The Clerk informed the resident that the greens are cut on the third Monday of each month from April to October inclusive.  Parish Councils have the right to determine what constitutes the level and depth of worded content that amounts to a record of the meeting.

Comments

Unless the rest of the meeting is minuted verbatim (god help us!), I'd say there is no right to have an item raised by a member of the public to have their question or statement recorded verbatim.
The public have a right to attend council meetings but not necessarily to speak at them although most councils do allow this.  However, unless the question or statement has been notified to the council in advance of the meeting, it's not going to be on the agenda so technically can only be noted and if appropriate referred to the next meeting or delegated to the clerk to respond separately.   In the real world of course simple questions etc. tend to be responded to.  If it's that important, the matter should be notified in advance so that it can be put as an agenda item.

Answer 2

Am I right in thinking the original question here has been changed as I'm sure the original asked about public questions or statements being reported verbatim?
Some councils hold their public questions/public participation outside of their formal meeting.  It's not recommended practice but it happens.  If that is the case here, then no, the question can't be included in the minutes as minutes reflect what happens in the meeting; not outside of it.