Correct Summary of Eevee Evolutions?

I want to make sure I understand the current rules of Eevee evolutions. From what I have read, I undertand as follows:
1. A player can use the name trick ONE time for each of the five evolutions types.
2. A player can make Eevee his or her buddy and walk that specific Eevee to obtain 2 candies (generally two 5 km walks) and then, while still using that specific Eevee as your buddy, evolve that specific Eevee during the night to produce an Umbreon or during the day to produce an Espeon, and this trick can be repeated as often as desired (not a one shot deal like the name trick).
3. Evolve an Eevee using neither of the tricks described above and have a one-fifth chance of evolving each type of Eevee.
I have read nothing about #3 above, but am guessing at it.
Does anyone have knowledge on the foregoing?
Thanks.