Какое бы решение начальница ни приняла, мы всё равно обсудим его спокойно.

It is a very common Russian pattern meaning whatever ..., no matter what ..., or regardless of what ....

So:

Какое бы решение начальница ни приняла
= Whatever decision the boss makes / may make

This pattern is often built with a question word:

• кто → кто бы ни... = whoever / no matter who
• что → что бы ни... = whatever / no matter what
• где → где бы ни... = wherever / no matter where
• какой → какой / какое / какая / какие бы ни... = whatever kind of...

It introduces a concessive idea: the main clause stays true regardless of the subordinate clause.

In this construction, бы and ни normally work together.

• бы helps create a non-factual, hypothetical, or open-ended meaning
• ни is part of the no matter... / whatever... pattern

So какое бы ... ни приняла is a set grammatical structure.

If you remove one of them, the sentence usually stops sounding correct or changes meaning:

• какое решение начальница приняла = what decision the boss made
• какое бы решение начальница приняла = incomplete / unnatural here
• какое решение начальница ни приняла = also not right in standard Russian

So for this meaning, think of какое бы ... ни as one package.

Because it agrees with решение, which is:

• neuter
• singular

The noun решение means decision and is a neuter noun, so the matching form of какой is какое.

Compare:

• какой план = what plan / whatever plan
• какая идея = what idea / whatever idea
• какое решение = what decision / whatever decision

So какое is there because of the grammar of решение.

Because решение is the direct object of приняла.

The verb phrase is:

• принять решение = to make a decision

That means решение is in the accusative case.

However, for neuter inanimate singular nouns, the accusative looks exactly the same as the nominative. So:

• nominative: решение
• accusative: решение

That is why you do not see any visible ending change.

This is one of the trickier but very common features of Russian.

In constructions with бы, Russian often uses the past-tense verb form, even when the meaning is not literally past. Here it expresses something like:

• whatever decision she may make
• whatever decision she ends up making

So приняла is formally a past-tense shape, but in this structure it does not simply mean ordinary past time.

You can think of it as part of a fixed irrealis / hypothetical pattern:

• что бы он ни сказал = whatever he says / may say
• куда бы мы ни пошли = wherever we go / may go
• какое бы решение начальница ни приняла = whatever decision the boss makes / may make

So the form looks past, but the meaning is broader.

Because the subject is начальница, which is feminine.

Russian past-tense forms agree with the subject in gender and number:

• он принял
• она приняла
• оно приняло
• они приняли

Since начальница means a female boss/supervisor, the verb must be приняла.

Yes, начальница means a female boss, female supervisor, or female manager, depending on context.

It is the feminine counterpart of начальник.

So:

• начальник = male boss / boss in a general masculine form
• начальница = female boss

In English we usually just say boss, but Russian marks the person as female here.

In English, we say it. In Russian, the accusative/genitive form of the third-person pronoun for a neuter thing is often его.

Here его refers back to решение.

So:

• решение = decision
• обсудим его = we will discuss it

This can feel strange to English speakers because его is also used for him and for masculine it in some contexts, but here it clearly means it, referring to the neuter noun решение.

Всё равно means all the same, anyway, or regardless.

Here it emphasizes that the action in the main clause will happen no matter what:

мы всё равно обсудим его спокойно
= we will discuss it calmly anyway / regardless

So the whole sentence has this logic:

• no matter what decision she makes,
• we will still discuss it calmly.

It is a very common phrase in Russian.

Обсудим is the perfective future of обсудить.

Perfective verbs in the future usually express a single complete action. That fits well here:

• обсудим = we will discuss it as a completed event

If you used the imperfective будем обсуждать, that would focus more on the process:

• будем обсуждать = we will be discussing

So обсудим is the natural choice if the speaker means one future discussion that will take place and be completed.

Спокойно is an adverb meaning calmly.

It modifies обсудим:

• обсудим спокойно = discuss calmly

So the idea is not that the decision itself is calm, but that we will talk about it in a calm way.

English often uses the same structure:

• We will discuss it calmly.

No, Russian word order is fairly flexible.

This sentence is natural as written:

Какое бы решение начальница ни приняла, мы всё равно обсудим его спокойно.

But you could move things around for emphasis, for example:

• Какое бы решение ни приняла начальница, мы всё равно обсудим его спокойно.
• Мы всё равно спокойно обсудим его.
• Мы его всё равно спокойно обсудим.

The core grammar stays the same, but the focus or rhythm changes slightly.

In the given sentence, the order is neutral and natural.

Because the first part is a subordinate clause:

Какое бы решение начальница ни приняла
= subordinate clause

and the second part is the main clause:

мы всё равно обсудим его спокойно
= main clause

Russian normally separates this kind of subordinate clause from the main clause with a comma, just as English often would:

Whatever decision the boss makes, we’ll discuss it calmly anyway.

Because this is not ordinary negation.

In this structure, ни is part of the fixed concessive pattern:

• кто бы ни...
• что бы ни...
• где бы ни...
• какое бы ... ни...

It does not simply mean not here. Instead, it helps create the sense of no matter... / whatever...

So:

• не = the normal negative particle
• ни = used in several special patterns, including this one

That is why не would be wrong here.

Not really. A very literal word-for-word approach will sound misleading in English because приняла looks past-tense but does not function as a plain past here.

A better natural translation is:

• Whatever decision the boss makes
• Whatever decision the boss may make
• No matter what decision the boss makes

So this is a good example of why Russian grammar should be read as a pattern, not translated word by word.