Мне больше ничего не нужно.

Because Russian usually expresses to need with an impersonal pattern:

кому? + нужно / надо + what

So the literal structure is closer to To me, nothing else is needed than to I need....

• мне = to me / for me in the dative case
• я would be the subject form I, which does not fit this pattern

So Я больше ничего не нужно is wrong, but Мне больше ничего не нужно is correct.

Here больше means any more, any longer, or anything else, depending on context.

It does not just mean the simple comparative more.

So this sentence can mean things like:

• I don't need anything else
• I don't need anything more
• I don't need anything anymore

In negative sentences, больше very often has this any more / no longer sense.

Yes, but in Russian that is normal.

Russian uses negative concord, which means that if you use a negative word like:

• ничего = nothing
• никто = nobody
• никогда = never

the verb or predicate also normally takes не.

So:

• Мне ничего не нужно = correct
• leaving out не would sound ungrammatical

This is one of the biggest differences from English.

Because ничего is the form normally used in this kind of sentence.

A simple way to remember it is:

• ничто is the dictionary form
• ничего is the form you very often see in real sentences like ничего не...

So ничего не нужно is the standard, natural expression.

You can think of ничего не... as a very common chunk meaning nothing ... / not anything ....

Нужно is the neuter singular predicative form meaning needed / necessary.

In this sentence it works as the core predicate: is needed.

Russian often uses нужно as a kind of default form in impersonal constructions, especially with words like ничего, что, всё, or with infinitives:

• Мне нужно уйти. = I need to leave.
• Мне ничего не нужно. = I don't need anything.

With specific nouns, Russian often uses agreeing forms:

• Мне нужна книга. = I need a book.
• Мне нужны деньги. = I need money.

So in your sentence, нужно is exactly the normal form.

Not in the way an English speaker might expect.

Russian often leaves out the present-tense verb to be, but in this sentence the main predicate is already нужно. So the sentence is complete as it stands.

You do not need to imagine an extra word inserted between не and нужно.

The whole idea is needed is already expressed by нужно.

Yes. Russian word order is flexible, and changing it usually changes emphasis, not the basic meaning.

For example:

• Мне больше ничего не нужно. = neutral, very natural
• Больше мне ничего не нужно. = stronger emphasis on any more / else
• Ничего мне больше не нужно. = stronger emphasis on nothing

So the original order is common and natural, but other orders are possible depending on what the speaker wants to highlight.

Both are natural and very close in meaning.

• Мне больше ничего не нужно.
• Мне больше ничего не надо.

In many situations they mean almost the same thing.

Very roughly:

• нужно can sound a bit more neutral
• надо can sound a bit more conversational

But in everyday speech, both are extremely common.

It depends on context, but because of больше, the idea is usually:

• I don't need anything else
• I don't need anything more
• I don't need anything anymore

If you removed больше, then Мне ничего не нужно would be more simply I don't need anything.

So больше adds the nuance of else / any more / any longer.

Only if you mean I don't want anything else.

That changes the meaning:

• Мне больше ничего не нужно = I don't need anything else
• Я больше ничего не хочу = I don't want anything else

Russian keeps need and want clearly separate here, just as English does.

So they are not interchangeable unless the context allows both ideas.