As-salamu alaykum, 

Does mixing up between [pronunciation of] letter-sounds which are similar nullify the salah [formal prayer]? 

Letter-sounds like:  ز , ظ ذ  ? Also ت , ط and also ث , س , ص and also د , ض and also ح , ه and also ا , ع also ق, ك . Does mixing up between these letters nullify salah? What about specifically mispronouncing the letter ذ as ز , ظ or the letter ث as س , ص ?

For [some] non-Arabs the letters ذ , ظ , and ث are quite difficult to pronounce since these letters are pronounced with a "lisp," i.e., bringing the tongue between the upper and lower teeth when pronouncing it. So [some] non-Arabs, because they are not used to the lisp sound, read the same representative sounds without the lisp.

In the name of Allah, the Most Merciful, the Grantor of Mercy

All praise belongs to Allah, and may prayers and peace be upon Allah’s final Messenger.

This answer pertains to the Fatihah only, since it is what is required for the salah (formal prayer) to be valid.

The majority of the scholars consider the salat invalid if one replaces a letter in al-Fatihah by another. Some scholars showed leniency with the letters that are close to each other in pronunciation. For example, some of the latter Hanafis and Shafi’ees showed leniency with replacing ت  by ط  , and Imam Ibn Taymiyyah indicated the same concerning ض and ظ .

These positions pertain to one who can learn the correct pronunciation. For one who cannot [learn it], Allah has said, 

}لا يُكَلِّفُ اللَّهُ نَفْساً إِلَّا وُسْعَهَا}

{Allah does not burden a person beyond his capacity.} [Al-Baqarah 2:286]

Allah knows best. 

Related fatawa: 79267, 86093, 87421