My experience is that children speak more simple than adults, and it´s often easier to learn a language by watching children speak.
Also, some childrens programs are of course aimed at teaching children to read which is great for us who wants to learn words.

So my question is: can you recommend any children´s programs or shows in Turkish, where children speak Turkish?

There are some Tv channels for children but they mostly have cartoons. Some channels show programs for kids but I don´t know when. I can give you some links to watch them. Some channels may not be broadcasting at night Or you can search videos of these programs, such as on YouTube. For example, Susam Sokağı (Sesame Street), or see below:

Planet Çocuk:

http://www.planetler.com/cocuk/Live.aspx

TRT Çocuk: (The first link shows which programs they have. You can see age groups and search them on the internet for videos)

http://www.trt.net.tr/trtcocuk/programlar.aspx

http://www.trt.net.tr/Anasayfa/canli.aspx?y=tv&k=trtcocuk

Minika:

http://www.minika.com.tr/minika_tv/minikacocuk

Yumurcak TV:

http://www.yumurcak.tv/

http://www.kure.tv/yumurcak-tv/Canli-yayin-izle/4/

Karamel TV:

http://www.karameltv.com.tr/canli.html

Animez: (This one is an anime channel. Japanese animes with Turkish subtitles. I don´t know if they have only Turkish ones)

http://www.yildiz.tv/?act=dvr&chan=kidz

I know that Caillou was translated in Turkish

And we have our own one -- Pepee

I watch the TRT series Keloğlan masalları. "The bald boy" is a traditional Turkish folk-tale hero and his adventures bring about many issues of general human interest. Keloğlan is a poor boy who is obliged to work while other children spend their days playing. He does not loose his spirit, though. He hears what animals have to say and respects the forest. He does not hesitate to help someone in need no matter if it is just an ant. That is why he finds a helper also when in trouble.

Even though Keloğlan is a story about hard life it always has a positive tone. "Kindness pays" it teaches.

Sihirli Annem (2003) !!