I hope I speak for the rest of the residence association when I say you are quite welcome to use the garden for a BBQ. We always welcome use of the garden as long as people are respectful to other residence and conduct themselves accordingly.
I am not sure if there is a BBQ in the East Block, but if you wish to use the West Block one, let me know and I will wheel it over for you.
I would also like to take this opportunity to wish you many happy returns of the day!
All the best