Kim ne derse desin, bu karardan vazgeçmeyeceğim.

Because they cover two different things:

• kim = who
• ne = what

So kim ne derse desin means something like no matter who says what. It is broader than just kim derse desin or ne derse desin. The speaker is dismissing both:

• who is speaking
• what they are saying

This is a very common Turkish concessive pattern. It often has the shape:

• V-se / V-sa + V-sin
• or with other verbs, similar repeated forms

Here:

• derse = if he/she says
• desin = let him/her say

But together, this is not understood literally as a real condition plus a command. Idiomatically, it means:

• whatever they may say
• no matter what is said
• say what they will

So kim ne derse desin is a fixed-feeling expression of indifference to others' opinions.

Because demek is somewhat irregular.

It can use different stems in different forms:

• der in the aorist/present-type forms
• de- in imperative/optative-type forms

So:

• derse comes from der + se
• desin comes from de + sin

That is why you get derse desin, not something like deerse desin.

-se / -sa is the conditional suffix.

Normally it means if:

• gelirse = if he/she comes
• yaparsa = if he/she does

But after question words like kim, ne, nerede, etc., it often helps create a no matter... meaning:

• kim gelirse gelsin = whoever comes / no matter who comes
• ne yaparsa yapsın = whatever he/she does
• kim ne derse desin = no matter who says what

So here it is not a real condition. It is part of a concessive structure.

Desin is the third-person imperative/optative form of demek.

Very literally, it means:

• let him/her say
• let them say

In this sentence, though, it is not a real command. It is part of an idiomatic pattern that expresses indifference:

• Let them say whatever they want; it makes no difference to me.

So the emotional force is more important than the literal grammar.

Yes, very much so.

A learner can understand it grammatically, but native speakers also process it as a familiar idiomatic pattern. Similar expressions are:

• Kim ne düşünürse düşünsün = no matter who thinks what
• Ne olursa olsun = whatever happens / no matter what
• Kim gelirse gelsin = whoever comes

So it is both:

• grammatically analysable
• highly idiomatic and common

Because vazgeçmek requires the ablative case: -den / -dan.

You vazgeçmek bir şeyden = to give up / back down from something.

So:

• bu karar = this decision
• bu karardan = from this decision

That is the form the verb needs.

Examples:

• Bu fikirden vazgeçtim. = I gave up this idea.
• Planından vazgeçmedi. = He/She didn’t give up on the plan.

So bu karardan vazgeçmeyeceğim is grammatically exactly what Turkish expects.

It breaks down like this:

• vazgeç- = verb stem, give up / renounce / back down
• -me- = negation
• -(y)ecek = future
• -im = first person singular

So:

• vazgeç-me-yecek-im
• I will not give up

The y appears because the negative suffix -me ends in a vowel, and the future suffix begins with a vowel.

Often yes, but context matters.

Vazgeçmek can mean:

• to give up
• to give up on
• to abandon
• to back down from
• to change one’s mind about continuing with something

In this sentence, depending on context, natural English might be:

• I will not give up this decision
• I will not back down from this decision
• I won’t change my mind about this decision

So the exact English wording can vary, even though the Turkish verb is the same.

Because Kim ne derse desin is an introductory subordinate clause, and the main clause follows it:

• Kim ne derse desin, = introductory concessive clause
• bu karardan vazgeçmeyeceğim. = main clause

In standard written Turkish, a comma is natural here, just as in English you would often write:

• Whatever anyone says, I won’t back down from this decision.

Yes. That is also correct and natural.

Difference in feel:

• demek is very common and compact in this pattern
• söylemek is slightly more explicit because it directly means to say / to tell

So both work:

• Kim ne derse desin
• Kim ne söylerse söylesin

The version with demek is especially idiomatic and very common.

Grammatically, desin is third person singular, but in this kind of expression it is often used generically.

Turkish often uses a singular-looking verb form in these indefinite patterns, especially when the meaning is broad and general rather than tied to a specific group. The important thing is the idiomatic structure, not strict number agreement in the way an English learner might expect.

So kim ne derse desin is the standard expression. You may hear other expanded forms in other contexts, but this version is the normal one here.