Is it possible to figure out why someone was murdered

I would suggest using a manager noble and the management screen (j, m) where you can queue up tasks. I find it useful to do thinks like:

• Queue 15 barrel
• Queue 15 brew drinks

And jobs that are managed are automatically re-assigned if they fail for any reason including lack of resources. So in this case the brew drinks would be re-assigned until the barrels are available to complete them.

Note that these tasks will process in parallel.

You can tame the small animal at the kennel, and then they can be used as pets. Some pets have a high value and can be used to make useless dwarves nobles happy.

To release the (now tame) animal use q to query the cage, a to assign, and then use enter to toggle the animal(s) currently inside (animals assigned to the cage will have a green + next to them). Any available dwarf will perform the job. (Source)