The elven trance does not reduce the time required for a long rest (as per Jeremy Crawford) — everyone requires 8 hours for a long rest. Note that a long rest does not actually require sleeping, just resting.
A short rest does not identify a magic items. Only an identify spell or experimentation will do that. The identify spell requires that the caster handle the item. This might activate a curse.
Note that activating a magic item is not a function of the "Use an Item" action. This means that features like Rogue Fast hands do not apply (DMG p141).
The Mixing Potions and Scroll Mishap tables are in play (DMG p140).
These must be some sort of physical item, and one created with care. Painting a god's symbol on a shield does nothing — it must be engraved or inlaid. Sticking a relic in a dirty old pouch won't do anything (except possibly angering the god) — it has to be a nice box or locket.
Holy symbols don't have to be blessed. They are not magical items and they don't require attunement.
Any cleric of Torm can use any holy symbol of Torm. The power is not in the symbol — it is in the person displaying the symbol and in the respect shown the relic.
These must be specially created to serve their role. A wizard can't just grab any old staff and use it as a focus.
These items are crafted using materials and shapes known to react strongly to magic. As with holy symbols, arcane focuses are not themselves magical nor does magic need to be used in their creation.
However, the knowledge of the materials and shapes is somewhat secret. Not every crafter is going to know how to create arcane focuses.
Staff focus items are usually built tough enough to be used as a weapon. Rod and wand items are, however, usually not built tough enough to be used as an improvised weapon.
Magical staves will say in their description whether or not they can be used as a focus.
This detects aberrations, as well as the classes of creatures listed.
If the sensed creature or place is behind total cover then the paladin just gets a vague sense of "something's there, that direction." The usual rules for detection apply (blocked by 2 ft rock, 2 in metal, etc).