So my question is: Was that the right way to do it? What are the chances that these daffodils will flower next Spring if I leave them in the ground.
Yes, you did the right thing. They may not bloom next season, or only part of them may bloom though as a result of them being dug so early. Though you left the foliage on them, it browned and died off prematurely I'm sure, thus the bulb was not fed as well as it could have been had they not been dug so early. The foliage here is still green and browning, and I don't think it will be prime digging, dividing/moving time until about the end of the month.

Also, I was given some daffodils in containers which are already brown. Do I cut the brown leaves off and plant them or dry them off and store them until Fall?
You can either plant them now, or store in a cool place and plant them in the fall after you cut the dead foliage off. I think either way is fine. I tend to try and do things when I am thinking of it and when I find the time. I would probably plant them now, if it were me.

Sue

Thanks Sue. That was what I thought and I feel the same about time being very limited. I will plant them now and hope to get some blooms next year. But if it just needs a year to spruce themselves up, I can wait. Even if just a few bloom, it will still look nice and all of these flowers were free...so no complaint here. Happy gardening!