Egm notice period

According to the provisions of the Companies Act there should be at least 21 clear days notice before the conduct of any general meeting of the shareholders. Notice should be sent at least 21 days before the date of the meeting. However what is required is that notice should be despatched to all the shareholders at least 21 days before the holding of the meeting. 

Yes, you can do so as there is no bar on maximum no. of days for notice period

Yes youy can do so. Companies Act prescribed minimum time gap of atleast 21 clear days.  Thus if you are giving more that that time it will be under the provisions of the Act, however, you cannot reduce such time gap except under shorter notice.