Both of these are DM calls.
So I'm wondering if a character could get drunk while wearing a PoPAP? There's no "drunk" status condition in D&D 5e, but drunkenness is caused because you've consumed enough alcohol to poison yourself, however slightly.
The problem here is that (outside of things that deal Poison damage or grant the Poisoned condition) there isn't any really great definition of poison. "The dosage makes the poison," and even water can cause intoxication and death in sufficient doses.
We usually bunch things that kill us with a "small" dose into the poison category, and things that kill us with a "large" dose into the not-poison category, but there's a lot of leeway in the middle.
Things that are immune to poison being immune to alcohol is a common trope. Alcohol isn't necessary for us to live, and has a variety of negative consequences. Thus, poison.
On the other hand, the effects of alcohol are pretty mild in typical dosages. It's unlikely to kill you, and may not even have a significant impact on you if you consume it slowly. Thus, not poison.
Which way the magic judges, is up to your DM.
Like for instance, if someone put spider venom in their food, would they know the food was poisoned when they ate it?
I think the general rule for spells applies well enough here. For spells, it works like this:
Unless a spell has a perceptible effect, a creature might not know it was targeted by a spell at all. An effect like crackling lightning is obvious, but a more subtle effect, such as an attempt to read a creature's thoughts, typically goes unnoticed, unless a spell says otherwise.
So, does the spider venom have a specific flavor, smell, or texture? The character can still discern that. If not, then the character doesn't get a "your amulet of poison has protected you" warning.
Of course, your DM could just as easily rule that you can feel the magic working. That there's a tingle in your stomach as the poison is attacked, or that the periapt glows, or similar.
Depends on the type of poison. If it's an injury poison, unless the wielder has a magical weapon that CAN pierce the skin, then, no. But if it's a CONTACT poison, well, looking at their immunities, they are NOT immune to contact poisons. So if I had a non-magical blade loaded up with a contact poison, just touching them would be enough to get the effect of the poison.
Types of poison in D&D 5 include, with my notes in italics:
Contact: Contact poison can be smeared on an object and remains potent
until it is touched or washed off. A creature that touches contact
poison with exposed skin suffers its effects. Therefore they suffer the effects if they are touched, no need for injury.
Ingested: A creature must swallow an entire dose of ingested poison to
suffer its effects. The dose can be delivered in food or a liquid. You
may decide that a partial dose has a reduced effect, such as allowing
advantage on the saving throw or dealing only half damage on a failed
save. Hard to do in combat.
Inhaled: These poisons are powders or gases that take effect when
inhaled. Blowing the powder or releasing the gas subjects creatures in
a 5-foot cube to its effect. The resulting cloud dissipates
immediately afterward. Holding one’s breath is ineffective against
inhaled poisons, as they affect nasal membranes, tear ducts, and other
parts of the body. Very effective against them, yes.
Injury: Injury poison can be applied to Weapons, ammunition, trap
Components, and other Objects that deal piercing or slashing damage
and remains potent until delivered through a wound or washed off. A
creature that takes piercing or slashing damage from an object coated
with the poison is exposed to its effects. Therefore, if no damage is taken, the poison cannot be delivered.
EDIT: However, in the comments, it's been pointed out that the lycanthrope immunity has less to do with not being able to pierce the skin at all and more to do with the fact that any non-magic/non-silver wound damage from those particular sources may close pretty much instantly. A DM could rule this way, but mechanics-wise, according to the rules, an injury poison would not work because it specifically states "a creature that takes piercing or slashing damage" and lycanthropes DO NOT take piercing or slashing damage from non-magic, non-silver weapons.
Best Answer
From Circle of Spores:
From Poisoned:
The druid cannot be poisoned: check.
From Damage Types:
Does the ability give damage resistance or immunity to poison damage: no.
Contrast this with Dwarven Resilience:
This is nice and clear compared to the UA stuff - but UA is often poorly drafted: maybe deliberately, maybe not.
The poisoned condition and poison damage are not the same thing. It may make thematic sense that someone who cannot be poisoned should not take damage from poison but if it doesn't say it it doesn't happen.