Correction: This rule was clarified in the Rules Compendium (page 110) with an updated wording.
You must decide what you want to do as you ready the action, not when you take the readied action.You can ready a standard action, a move action, a swift action, or a free action. To do so, you must specify what you want to do and the conditions under which you will do so.
As for synchronicity, the same applies: unless you augment the power, you have to decide what you want to do when you ready the action, not when you take it. If you do augment the power, then you can wait to decide.
Unclear, but the use of the phrase "permanently modify" suggests the answer may be no. On the other hand, that interpretation may result in dysfunctions, e.g. being unable to manifest the power without expending psionic focus. Consult your DM.
It depends on the item, but generally, if the effect refers only to part of a spell's effect, it's only referring to that part of the spell's effect. In your example of the binding weapon, it prevents extradimensional travel as if the target were affected by dimensional anchor, but it doesn't duplicate any other aspects of dimensional anchor—you do not need to make a touch attack roll or a spell penetration check. Another example is the granted ability of the Travel domain, which allows you to ignore magical impediments as if you were under the effect of freedom of movement, but does not grant you any other benefits of the spell, such as the ability to automatically resist grapples or move normally underwater.