Would a small group be able to have a free yoga event in the park?

I guess yes why not, this Gina be fantastic ;)

Yes, I don't see why not. There are lots of open areas

I don't see why not. You would want to find out in advance if the area you plan for your activity will be unoccupied that day . It may be possible that other large advertised events could be using the space. It is a large place with many different segregated and blended areas.

There is plenty of space as well as opportunity

Yes you can

Yes