Why we should use "же" in this sentence:
где же ручка?
Without "же" this sentence is also complete!
And also I saw in another sentences, too.
And "же" means same or again?
Here же is an emphatic intensifying particle.
Где ручка? is a straight question.
Где же ручка? may be an expression of 1) impatience, frustration and annoyance of not being able to find it (Where's the pen for god's sake?) or 2) surprise about its disappearance or inability to find it (So where's the pen?)
You use "же" for amplification, or for making the question softer, to ask a rhetorical question. In everyday speech "же" is used only for amplification and is often supplemented with words "правда", "на самом деле" to underline the meaning:
"Я же говорил!" - "I've really told you that"
"Он же не справится!" - "He won't be able manage it for sure"
"Я же правда туда ездил!" - "I really went there!"