Следовательница поняла, что преступление было не случайным.

Yes. Следовательница means female investigator.

It is built from следователь + a feminine suffix. A native speaker may use:

• следователь = investigator
• следовательница = explicitly female investigator

A useful nuance: in official or neutral Russian, profession words are often kept in the masculine form even for women, so следователь can still refer to a woman. Следовательница is possible and clear, but it sounds more explicitly gender-marked and can feel a bit more conversational or stylistically noticeable.

Because the verb is in the past tense, and in Russian past-tense verbs agree with the subject in gender and number.

The subject is следовательница, which is feminine singular, so the verb must also be feminine singular:

• понял = he understood / realized
• поняла = she understood / realized
• поняли = they understood / realized

So следовательница поняла means the female investigator realized.

Because поняла comes from the perfective verb понять, which usually expresses a completed result: she came to understand something, she realized it.

Here the meaning is a moment of realization:

• поняла = realized, understood
• понимала = was understanding / understood in an ongoing sense

So this sentence is not describing a continuing state of comprehension. It is describing the point when she figured it out.

Что here means that and introduces a subordinate clause.

So the structure is:

• Следовательница поняла = The investigator realized
• что преступление было не случайным = that the crime was not accidental

The whole что-clause gives the content of what she realized.

Because Russian normally uses a comma before что when it introduces a subordinate clause.

So:

• Следовательница поняла, что...

This is standard Russian punctuation for a complex sentence: main clause + subordinate clause.

Because inside the subordinate clause, преступление is the subject of было.

Even though the whole clause что преступление было не случайным is the thing she realized, the words inside that clause still follow their own grammar:

• преступление = subject
• было = verb
• не случайным = predicate description

So преступление stays in the nominative.

Because преступление is a neuter singular noun, and the past-tense form of быть agrees with it:

• masculine: был
• feminine: была
• neuter: было
• plural: были

Since преступление is neuter, Russian says:

• преступление было

Also, remember that Russian usually drops to be in the present tense, but in the past tense it is expressed:

• present: преступление случайное or преступление неслучайное
• past: преступление было случайным / неслучайным

Because after быть in the past tense, a noun or adjective used as the predicate is often put in the instrumental.

So:

• преступление было случайным
• преступление было не случайным

This is a very common pattern in Russian.

Here случайным is the instrumental singular form of случайный. Since the noun is neuter singular, the instrumental adjective form is still случайным.

A learner often expects something like случайное, but that would normally be used as an attribute before the noun:

• случайное преступление = an accidental crime

After было, Russian normally uses the predicate form in instrumental:

• преступление было случайным = the crime was accidental

Because не случайно is usually adverbial/predicative, meaning something like not by chance.

Compare:

• Это было неслучайно = It was not accidental / It did not happen by chance.
• Преступление было неслучайным = The crime was not accidental.

In your sentence, Russian is describing the noun преступление with an adjective, so случайным fits better.

So the difference is roughly:

• не случайно / неслучайно = not by chance
• не случайным / неслучайным = not accidental

They are close in meaning, but grammatically they are not the same.

This is a very good question, because both spellings can appear, but the nuance differs.

Usually:

• неслучайным written together = a regular opposite meaning, not accidental
• не случайным written separately = stronger negation, contrast, or emphasis

For example:

• преступление было неслучайным = the crime was not accidental
• преступление было не случайным, а тщательно спланированным = the crime was not accidental, but carefully planned

In a neutral sentence like this one, many native speakers would probably prefer неслучайным as one word. The separate spelling in your sentence can suggest an implied contrast or simply a stylistic choice.

Yes. Russian word order is flexible.

For example, these are both possible:

• Следовательница поняла, что преступление было не случайным.
• Следовательница поняла, что преступление не было случайным.

The meaning is almost the same. The difference is mostly one of emphasis:

• было не случайным puts the negation a bit more on the predicate quality
• не было случайным puts the negation a bit more on the whole predicate

Both are natural Russian.

In general, случайный can mean things like:

• accidental
• random
• by chance
• coincidental

With преступление, it usually means something like:

• not accidental
• not random
• not the result of chance
• probably deliberate / intentional, depending on context

So in this sentence the idea is that the investigator realized the crime was not just some chance event.