Yes, your dentist should have used a rubber dam to not only keep things from going down your throat but to also keep the area sterile. The dentist should have flushed the roots out with a solution of water and bleach, he/she then would have left cotton pellets that have been soaked in a sedative/antibacterial solution under the temporary filling.

Your tooth will be a little tender for the next day or two, it's had a lot of filing and reaming done inside the roots. You can take some Ibuprofen or Tylenol if you need to.
It surprises me that they did not schedule the next appointment. It should be within the next 7-10 days if the tooth is feeling fine.

Tickle is right, a crown should be done after about 6 months (you want to be sure the infection has cleared up). This will keep the tooth strong and prevent it from breaking. Once the nerve has been removed, there is no moisture inside the tooth and it can become very brittle and break easily (depending on where it is in your mouth and your occlusion(bite)).

I hope this helps. Call your dentist today and have them schedule the final root canal appointment. These days root canals are usually completed in one sitting if there infection isn't excessive.