[RPG] How many Encounter Powers can I use during an Encounter

You were correct -- by the book, you can absolutely use encounter powers outside an encounter. Healing powers are the most common example of this, but there are others -- for example, the bardic power Words of Friendship, which gives you a boost to Diplomacy, is almost always going to be used in non-encounter situations. As @veritascitor points out, an encounter power is just a power that can be used once every five minutes in non-stressful situations.

Bear in mind that if you use Healing Word after a short rest, which is a must for Restful Healing, you don't immediately recover it. You'd need to take another short rest to get it back. Sometimes you'll have another five minutes to spare; sometimes you won't.

Something else that might come up in this regard is the duration of powers that last until the end of the encounter. Page 278 of the Player's Handbook covers this: they last "when you take a rest (short or extended) or after 5 minutes."

Finally, if your group has a house rule that says you can't use powers outside combat, well... then they have that house rule. I'd point out the example you noted, and cite Words of Friendship, but in the end every group does have the right to come up with their own variations on the rules.

You must only prepare spells that are different levels within a power type (Encounter, Daily or Utility). Example: You have a spellbook that lists 2 - 14th level spells as available to your character to prepare. In preparing spells for the day you can only prepare one of them, period.

You would not necessarily have different levels between power types. Example: You might a have a 1st level Encounter and a 1st level Daily prepared. You would not have 2 1st level Daily's prepared.

Added per Request From comments below:

Yes. DDI: "Spells Prepared per Day" table shows how many encounter, daily, and utility powers you are allowed to prepare each day. You cannot prepare more than one power of any given level on the same day. For example, a 14th-level mage who has taken the enigmatic mage paragon path can prepare four encounter attack powers per day. Her spellbook contains multiple encounter attack powers at various levels. She can prepare four powers from any of the levels, as long as none of the prepared powers are of the same level. Treat each power type (E.D.U.) separately.

Your example: "Her spellbook contains multiple ENCOUNTER attack powers at various levels. She can prepare..." is the key to the answer.