Trying to answer these.
Hawkman- All I know is the actor has posted some workout videos.
Arrowverse- They ordered pilots for 3 new shows and picked up 1. This means they are still making shows and are continuing a new show a year. Of their last 3 new shows one is S % L, which is a big hit. One is Stargirl which was number 2 in CW streaming. The other is Batwoman which was number 3. They are very much alive and seemingly building for a future of Superman/Stargirl/Batwoman/Naomi/Legends.