Can someone explain me the differnce between these three -

diðer baþka öteki?

Thank you in advance

 A quick example in English, but wait for someone like caliptrix to give a really good grammatical explanation.

Baþka: is like "another one". It is more general and means any item that is different from the one you are referring to.

Bu kalem çalýþmýyor, baþka kalemin var mý?

this pen doesn´t write, do you have another pen?

Öteki: "the other one". Specifically the other one out of a choice of two.

Ahmet Bey´in iki kýzý var. Biri doktor öteki öðretmen.

Ahmet Bey has two daughters. On is a doctor, the other a teacher.

Diðer: "other"

Good explanation. There are a few words with similar functions:

ADJECTIVE   (-ADVERB)

öbür - ü

öteki - si

baþka -sý

diðer-i

THE OTHER:

Bu olmaz öbürünü/ötekisini ver. This is not good, give me the other one.

Ayýn öbür yüzü. The other side of the moon.

Diðeri nerede? Where is the other one?

ANOTHER

Bu olmaz. Baþka yok mu? This is not good. Isn´t there another one?

Hayayýnda baþkasý var mý? or Hayatýnda baþka biri var mý?

Is there another person in your life?

OTHER

Diðer günler hep boþum. I am completely free on other days.

Diðer taraftan. On the other hand.

I agree with your explanations. But you can use "diðer" also as "the other". I think (I couldn´t find any exceptions now) you can always replace "öteki" with "diðer" or "diðeri"

e.g.

She saw two dresses; one blue, the other red. She tried the red one but she bought the other dress.

Ýki elbise gördü; biri mavi, diðeri/öteki kýrmýzýydý. Kýrmýzý olaný denedi ama diðer/öteki elbiseyi aldý. (or Kýrmýzý olaný denedi ama diðerini/ötekini aldý.)