Nice to see you're still running the fortress and uploading videos! A few tips since you asked for help:
Building the goblin cages for the arena: when you start placing a cage and see the list of available cages, hit x to expand the list, and then you can pick a specific cage that has a trapped goblin inside.
This works for everything you can build in game, so you can for example pick only the best tables and chairs for your legendary dining room or use an artifact bed for your baron's bedroom. You can even select individual stone blocks for building workshops or walls and such, if you want. Also very useful for building weapon traps, as you can select only the best mechanisms and weapons for the traps.
Before you let the goblins out of their cages, you might want to disarm them. See the
wiki.
Viewing artifacts: hit l to see the list of all artifacts made in your fortress. No need to search through the stockpiles. Hit enter to view the artifact's value and then v to view what it is made of.
Butchering animals: hit z to go to the status screen, select the animals tab, hilight an animal and hit b to mark it to be slaughtered.
Infections and injuries: Hit v, point to a dwarf and hit w to see their injuries. Scroll up/down with -/+ keys. I think infections are listed there too. Anyway, if you have the chief medical dwarf appointed, you can use the
health screen. Hit z and select the health tab. You can scroll the list left and right and hit enter to see the health of a specific dwarf or animal.