Amulet of Proof vs. Detection and Location - The amulet, and spell, protect from magical divination and mental or magical location. 'Mental' being psionic or psionic-like powers, see the list in the item description. I don't see any explicit or implied text that says it keeps you from being heard, smelled, felt, or seen by those with natural senses that make that possible. This would include a character's natural chance to detect invisible based on level and intelligence.
Dead Stone – a small greyish stone, when placed in the mouth, allows the user to speak with dead without any limits, as long as any tiny bit of the remains of the dead creature is touched. Note this means language, time and planes are not barriers.
Hat of Difference - if a character wears this hat at any time during an event where experience is earned, all experience from that day is applied to the 'Hat' class. This is to keep me from having to microfiddle to keep up with what experience points go where. Note you can't put the hat on for a second, take it off, and put experience into the 'Hat' class - it has to be worn during an experience earning event. This item is ripe for abuse, so let's not make me get picky about the use of the item.
The Hat of Disguise will also allow the wearer to change the appearance of their clothing and gear, from head to toe, in addition to the bodily changes such as race, hair, skin, and so on, within the limitations of changes to height and weight as described in the UA. Note that this changes the appearance only - no actual physical change happens, it is a visual illusion only. This will not change, for instance, the sounds a person makes when moving or walking, the smells of their gear and body, or the way they feel to anyone who touches or strikes them. As such, it could be seen through with magical sight or various types, as spells cast at 16th level of use (the minimum needed for the Permanence used to make the item).
Jewel of Flawlessness - as gems in my game are generated from a computer program, and the chance to increase value has already been checked, this item doesn't work quite like the DMG description. In order to use it, it should be placed touching one or more other gems. Each gem has a 10% chance to go up one category of value, per the gems tables on DMG page 25 and 26. Any gem which does not go up in value cannot ever do so; any gem which DOES go up in value can be tried again, but if the value doesn't chance, those gems are now unable to be affected by this magic item.
Well of Many Worlds
Roll a D20 for where the well opens up to each time it is opened. If left in place, it will open to the same destination.
1-2 parallel world, very similar to the one where the Well exists
3-4 parallel world, different from the one where the Well exists to a noticeable degree, either in climate, power of magic, presence of certain creatures, degree of technology, or gravity. Differences will not be fatal or incomprehensible, but noticeable with some exploration.
5-6 parallel world, different from the one where the Well exists to a great degree, as above. Even chance that the changes are more hostile than the source world, or more pleasant than the home world, but the change will be major.
7-8 parallel world, different from the one where the Well exists to an extreme degree, as above. Even chance that the changes are more hostile than the source world, or beneficial. Hostile changes might be quickly harmful or even deadly.
9 a different world, very similar to the one where the Well exists
10 a different world, different from the one where the Well exists to a noticeable degree, either in climate, power of magic, presence of certain creatures, degree of technology, or gravity. Differences will not be fatal or incomprehensible, but noticeable with some exploration.
11 a different world, different from the one where the Well exists to a great degree, as above. Even chance that the changes are more hostile than the source world, or more pleasant than the home world, but the change will be major.
12 a different world, different from the one where the Well exists to an extreme degree, as above. Even chance that the changes are more hostile than the source world, or beneficial. Hostile changes might be quickly harmful or even deadly.
13 a different plane, randomly determined from the list of Inner planes (including the Astral or Ethereal), but one that is not immediately hostile in environment. However, there is an even chance that the denizens will be friendly or hostile if met.
14 a different plane, randomly determined from the list of Inner planes (including the Astral or Ethereal), one that is somewhat hostile in environment. However, there is an even chance that the denizens will be friendly or hostile if met.
15 a different plane, randomly determined from the list of Inner planes (including the Astral or Ethereal), one that is quite immediately hostile in environment. However, there is an even chance that the denizens will be friendly or hostile if met.
16 a different plane, randomly determined from the list of Inner planes (including the Astral or Ethereal), one that is likely fatal in environment. However, there is an even chance that the denizens will be friendly or hostile if met.
17 a different plane, randomly determined from the list of Elemental planes, but in an area of that plane that is not a hostile environment. However, there is an even chance that the denizens will be friendly or hostile if met.
18 a different plane, randomly determined from the list of Elemental planes, but in an area of that plantethat is not a pleasant environment. However, there is an even chance that the denizens will be friendly or hostile if met.
19 a different plane, randomly determined from the list of Elemental planes, but in an area of that plane that is a somewhat hostile environment. However, there is an even chance that the denizens will be friendly or hostile if met.
20 a different plane, randomly determined from the list of Elemental planes, but in an area of that plant that is a very hostile environment, probably quickly fatal. However, there is an even chance that the denizens will be friendly or hostile if met.