No answer seems to get the full picture, so let's do a summary.
Here is what happens to your items after you die: Items can be picked up.
When you die, all the items in your inventory are dropped on ground.
Items on the ground are destroyed by explosions (creepers and TNT), lava and cactus.
Items float as of the recent Update Aquatic.
Water streams also move items.
Items on the ground get deleted after 5 minutes.
Items are affected by gravity and have no explosion resistance, health, etc.
which other blocks/objects have.
This means that even after they are dropped, a small explosion can kill all of them.
Items placed in a chest are stored infinitely until removed, or until the chest is destroyed.
The rules above then apply to the items dropped.
Chests cannot be destroyed by fire, lava, or water, but can be destroyed with explosions.
The rules listed above do not apply if the chunk is unloaded.
After you die, if you had any experience on you, you can retrieve a fraction of it.
gaming.stackexchange.com/users/23/badp
Your inventory is scattered around your death spot, and will stay there for approximately 5 minutes.
Run for it!
gaming.stackexchange.com/users/1847/yatima2975
When you die by Creeper-explosion the items in your inventory are destroyed.
If you die by any other means they are scattered and can be recovered.
gaming.stackexchange.com/users/3651/Nicolaya
To answer your three bullets: Is my inventory lost forever after death?
When you die all of your items scatter on the ground.
On respawn you can go and pick them back up
but they stay on the ground for a limited time.
Unfortunately, if they disappeared then they are gone forever.
You can take advantage of this while raiding a dungeon, just charge in with a sword and upon dying run back to the dungeon, pick up your sword, and try again.
Does storing items in chest help them persist after a respawn?
Items in a chest remain in-game forever, or as long as the chest persists.
So anything you have stored in a chest will be there after a respawn.
What happens to the contents of a chest if it is destroyed?
If a chest is destroyed its contents, and the chest block, will spill on the ground and can be picked up.
If it's an explosion that destroys the chest, some of the spill will be lost.
Chests are not affected by fire.
gaming.stackexchange.com/users/1721/Sadly Not
After you die, the contents of your inventory is lost.
Items placed in the world, such as in chests are safe and you can rest easy knowing they will not despawn unless the chest is destroyed (i.e. by Creeper explosion).
It is for this reason among others, that one of the first tasks suggested to every Minecraft player is to build themselves a small home, in which they can rest safely at night, and store any valuables not needed on a current expedition.
gaming.stackexchange.com/users/3129/LessPop_MoreFizz
There is a small problem with all of these answers: they are slightly incorrect.
When you die, Lava and exploding creepers may destroy some or all of your items immediately.
The rest are scattered on the ground around you, and a five minute timer starts (even while you are on the death screen).
This timer counts down as long as the chunk the item is in remains loaded into memory.
For performance reasons, approximately a 20x20 block of chunks around the player are loaded into memory at one time (about 320x320 blocks, with you in the center).
If your bed/spawn is farther than 160 blocks away, then the timer on those fallen items pauses when you respawn, and it will not begin again until you get within 10 chunks and the area they are in is reloaded into memory.
In single player, this means that the items will almost certainly survive until you return, as long as you do not dally, regardless of how far away they are.
However, in multiplayer you are not the only person in the world...
having someone else in the same general area as your fallen items will cause the timer to continue to count down, even if you are very far away.
But this is only for items that are on your person (and thus fall on to the ground when you die); items in chests remain permanently across saves and deaths.
If the chest is destroyed they all fall on the ground around the chest, and the same 5 minute timer and rules about the chunk being loaded apply.
gaming.stackexchange.com/users/1936/Myrddin Emrys
If a chest is destroyed by you mining it, the contents will fall on the ground as if you died.
(scattered on the ground)
Cactus, fire, and lava can destroy those items.
If you was blown up by TNT or Creepers
your inventory will be perfectly fine, for the explosion hits you and then your items come out.
Believe me, I've been through my fair share of explosions.
Hope this sets things straight.
gaming.stackexchange.com/users/None/
Is my inventory lost forever after death?
Once you have died your items will be scatters around your death spot for 5 mins, but if you die in lava it will all be gone forever.
Does storing items in chest help persist them after a respawn?
Storing stuff in a chest is usually a wise idea, mainly if your going into uncharted areas, like caves.
You stuff will all be safe.
Note: Always try to stay near spawn point, so if you die you can run inside fast.
What happens to the contents of a chest if it is destroyed?
If a chest is destroyed all your stuff will be on the ground, in any case its kind of like dying, it will only stay for 5 mins.
If I am correct, chest can only be destroyed by you for TNT, and creepers.
gaming.stackexchange.com/users/None/
I've died a few times before reaching the point where I can get some action going; after each death I was unable to recover the contents of my inventory.   Is my inventory lost forever after death?  Does storing items in chest help persist them after a respawn?  What happens to the contents of a chest if it is destroyed?
What persists after a respawn in Minecraft?
gaming.stackexchange.com
<minecraft-java-edition>
gaming.stackexchange.com/questions/7744
gaming.stackexchange.com/users/23/badp
The contents of your inventory are lost after you die. They stay around for 5 mins after and are then deleted. Items stay on the ground after your death for 5 minutes, however they may be lost instantly according to some people.
This user suggests that the inventory is lost The majority think that the items despawn after 5 minutes.