[RPG] Calculating critical hit damage

I was inspired by @gomad's answer to check the Bestiary. There's nothing directly applicable, but there is an Animal Critical Miss Table (eg. 9, 10, 11 - animal slightly off balance, defends at -2 until its next turn; 18 -animal fails so badly that it loses its nerve and flees if possible). The book suggests alternatively using the normal Critical Miss Table, treating any 'weapon breaks', 'weapon dropped' or 'weapon turns in hand' as 1d-3 damage to the animal (my emphasis).

From the PHB (p. 196):

Critical Hits
When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.
For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.

The example given answers your first question perfectly.

For the spider, the secondary damage is from poison, so is not inherently part of the attack. This can be seen by the fact that the damage doesn't depend on the attack roll, but a separate saving throw.
Critical hits represent hitting a vulnerable area. With poison, it doesn't really matter where you are hit.