Mektuba pul eklemeden göndermemelisin.

The -meden here is a negative adverbial participle (zarf-fiil) suffix meaning “without doing.” It’s built from:

• the verb stem ekle- (“to add”)
• the negative suffix -me-
• the ablative suffix -den (becomes -den by vowel harmony)

Together ekle- + -me- + -den = eklemeden, literally “without adding.”

göndermemelisin breaks down into four pieces:

1. gönder- (verb stem “to send”)
2. -me- (negative marker “not”)
3. -meli- (necessity/obligation marker “must/should”)
4. -sin (2nd person singular ending “you”)

Put together, gönder-me-meli-sin → göndermemelisin, meaning “you must not/send – you shouldn’t send.”

In Turkish, the dative case (-a/-e) marks the indirect object or “to whom/what” something is sent.

• mektup = “letter” (nominative)
• mektup + -a = mektuba = “to the letter”

So mektuba göndermek = “to send (something) to the letter.”

Yes. A common alternative is koymak (“to put”).

• Mektuba pul koymadan göndermemelisin.
  Both mean “You shouldn’t send the letter without putting a stamp,” though eklemek (“to attach/add”) is slightly more precise.

• gönderme! is a direct negative imperative: “Don’t send!”
• göndermemelisin expresses advisability or obligation: “You shouldn’t send.”

The first is a command; the second is more like giving advice or stating an obligation.