I've tried to make a danger room trap, only to be told there are no palm training spears
When a bin sitting in the general stockpile is full of palm training spears
You have 1 of a few problems:
1)You have already used up all your spears, but they haven't been installed yet. Make some more.
2)Your spears have been assigned to your military, make some more/de-assign them.
3)Either your spears or your trap room can't be reached from the other. Check to see if both are accessible.
4)The spears or bin is forbidden. Unforbid it.
5)The bin has been selected for a hauling task, check back in a while and possibly check the job screen and try to find a "store item in bin" task that matches your bin.
6)Your game is broken. Very highly unlikely, but possible. Regen a new world.
With seeds, I'm still trying to fix the 'no plump helmet spawn' when there are barrels full of plump helmet spawn
You can remove 99% of these problems with a simple dual stockpile setup.
1)Stockpile 1 takes from anywhere and gives to stockpile 2. Barrels are not enabled.
2)Stockpile 2 takes only from links. Barrels are enabled.
Stockpile 1 can be a small stockpile (1-5 squares) and stockpile 2 can also be a small stockpile (since seeds fit in barrels at a very high ratio).
Storing your seeds should then work like this:
1)Dwarf notices a seed, checks stockpile 1 and sees that the stockpile is empty. It then grabs the seed and hauls just it to stockpile 1 (without grabbing any bags or barrels.
2)Dwarf realizes that it can carry this seed it just dropped in stockpile 1 to stockpile 2 where it can be stored in a bag/barrel.
3)Dwarf grabs the bag/barrel for the briefest of instants, walks 1 tile to grab the seed and 1 tile back to drop the barrel/bag back in stockpile 2.
Unless your farmer happens to try to grab a seed in those 5 seconds when the dwarf is carrying the seed those 2-5 tiles from stockpile 1 to stockpile 2, this will not generate any cancellation messages.
On the exact topic of bins, I've never had any problems or drawbacks with them, and their benefits greatly outweigh any potential slowdowns they might cause.