In general, this is messy and is left to the DM to adjudicate. There have been rulings for some of these, and others they refused to answer because they aren't sure if the RAW needs to be changed or not and are still examining the question themselves. So, the overall answer, the "What counts as part of the attack" here is as clear as mud. And additions to the Errata are rare on purpose, so don't expect it getting cleared up anytime soon.
They have stated in tweets that they don't fear or mind large spikes in dealing damage, but frown on large sustained gains to dealing damage.
Yes, it is part of the attack.
Any dice that are part of an attack's damage are rolled again on a crit.
Can a Paladin hit with a crit, and then choose to use smite and double all his dice? Yes, it is part of the attack.
Here we get into the weeds. It isn't clear because what they intended and what made it into the books differs.
The intent is no. The saving throw, not the attack, determines whether the poison takes effect after a hit.
The intent is no, but what is the ruling? Well, there isn't one:
I'm not ready to give the official answer, since this is part of my potential-errata analysis.
Perhaps because that was in 2015, and no poison additions were made, we are to expect that poison RAW is doubled, even though RAI it is not.
See poison's messy situation in my section on Poison. I think the same is true there: RAW yes, RAI no.
I've not seen this one answered, and looking at it I don't see how it would be different from a normal smite, but it COULD be looked at in the same light as poison.