I cannot help with #1. This was a snap shot I took from a YouTube video of "Royalty at Work" part 2 of 5, time frame 21:55. Maybe view the video for a better look. There is only a brief glimpse of the brooch. I can see where people think it is a Grenadier badge - but I do not think so.
#2 - Girl Guide Gift brooch. I have 2 dates for this brooch and outfit 29Jan1950 for a visit to Girl Guide Headquarters and 18Oct1951 on HRH's visit to Canada