Yes, Memluk means slave, servant.  mamlūk مملوك -->

 It is passive participle of  the verb 

ملك

Because, the sentence has no context, it is naturally missing other elements such as zaman, place…..etc.  

But, it is grammatically correct and regular sentence.

Say, you lived in Turkey for five years and you became a Turkish citizen. Officially your country is Turkey. But , in fact you are originally from England. One day , when you move back to your country, your Turkish friends will say " O, memleketine geri döndü."  What they really mean is " He´s gone back to his fatherland ".

Or , take  someone who was born and lives in a village in Trabzon. He moves to Istanbul to work. He settles in Istanbul and after long years he decides to go back to his memleket [a village in Trabzon where he originally come from"]

Memleket is an Arabic origin word which comes from the root "mülk" ملك [possession,property], it means " the thing that is possessed", kingdom . However, at present day , that word means " home country , home town , father´s country , the place you come from " .

Ülke is a Turkish origin word which means again "country".

The difference is seen in practice, for instance ;

* "memleket"  is used when to ask someone where he/she does come from ? 

- Memleket[in] nere ? ---> Where do you come from ? 

we can not use "ülke" in this context. 

Memleket is more informal  than ülke. Therefore ;

* When we give the official statistics , we prefer "ülke" ;

Ülkemizde meydana gelen trafik kazaları çoğunlukla sürücü hatalarından kaynaklanmaktadır. 

The traffıc accidents that happens in our country is usually caused by drivers fault. 

There is an old thread relating that issue. Check this out ;

http://www.turkishclass.com/sfa/turkce/forumTitle_1466

çoktandır -> for long time

Rica ederim.

Şiir yazmak gerçekten zor iş. Ama sende yetenek var.

Then, instead of repeating "diye" twice [ne var diye sordum diye...] it is better to say " ne var diye sorduğum için......" ---> because I asked it [them] saying what´s the matter .....

Yani "yağmurdan ilham aldın"  --->  You got inspired by rain.

Yani sana ilham geldi..