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Not really - memleket is generally used to mean ´home town´ or ´home land´, and could refer to a country, region or even village.

Ulke is country or land.

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. 

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

 It is passive participle of  the verb 

ملك