Slightly different answers here.
1) Unless the spell says otherwise, yes. Some spells block detect magic and other divination. Also, the person casting Detect Magic can fail to perceive a magic aura if the person that placed it attempted to conceal the aura through mundane means, like hiding it.
2) There are some spells that say they are exceptions.
3) It can work that way, but it can also fail. Dispel Magic always has a chance to fail. Also if the magic trap is the type that resets itself, dispelling the trap only disables it for a short amount of time. Typically only for 10 minutes, an hour or 24 hours. Some traps say how long it takes to reset, others the GM has to make a decision. Not all magic traps reset, some only go off once.
4) Read the description of the item. A lot of items are based directly on a spell, but an equal amount of them give restrictions or additional provisions that override the spell description.
That said, if the item casts Animate Dead and has a Caster Level greater than 5 (CL:5 or more), you can animate double the CL in Hit Dice (HD).
The spell targets one or more corpses. It turns them into Skeletons or Zombies by applying to template to the creature as if they were still living. That means to get a 10 HD skeleton or zombie, you need the corpse of a 10 HD creature to animate. You can't take the corpse of a 10th level human and create a 10 HD skeleton because humans are only 1 HD. Class Levels are not Hit Dice. You only get the base race plus any templates applied to the creature when you use animate dead.
