It is common practice for Clerks to send minutes to the Chair of the committee for their review as it helps uncover any mistakes.
However minutes are the official record of the meeting as made by the Clerk and not by the Chair. Some Councils would then send out the draft minutes to the relevant Councillors for their reference and other Councils would include them in the agenda pack for the next meeting (therefore sent out in advance of the meeting so that the Councillors can do their prep)
Minutes are then presented at the next meeting for approval by the Committee before they are signed by the Chair as an accurate record. It is at that point that any amendments should be requested, and noted on the official copy before being signed. Interestingly, you might want to note that it is down to the Clerk to accept any changes to the minutes and they can refuse the amendments. If this is the case, then the Chair would sign the minutes with a statement to that effect.
As for Standing Orders, it is up to the council to add anything that they feel is appropriate for the running of their particular Parish. In the model standing orders, there is a whole section relating to draft minutes and their approval (Section 12). If you don't have this in your standing orders, you might want to raise the issue as it is important.
