Теперь я понимаю то, что в начале показалось мне странным: у свидетельницы было слишком спокойное лицо.

То, что is a very common Russian pattern meaning what / that which / the thing that.

So:

• Я понимаю то, что... = I understand what...
• literally: I understand that thing which...

In English, we usually do not need both parts, but Russian often does. Here то points to the content, and что introduces the clause that explains it.

A few comparisons:

• Я знаю, что он прав. = I know that he is right.
  Here что simply introduces a content clause.

• Я знаю то, что он сказал. = I know what he said / the thing that he said.
  Here то, что refers to a specific thing.

So in your sentence, то, что в начале показалось мне странным means the thing that seemed strange to me at first.

Here в начале means something like at first or in the beginning.

Yes, in many contexts you could use сначала with a very similar meaning:

• Сначала это показалось мне странным.
• В начале это показалось мне странным.

Both can mean At first, this seemed strange to me.

Why write it separately here?

• в начале is literally in the beginning
• it is a preposition в
  • noun начало
• separately written forms often feel a bit more literal or contextual

There is also вначале as a single-word adverb, meaning at first. So learners often see three possibilities:

• сначала = at first
• вначале = at first
• в начале = in the beginning / at the beginning

In this sentence, в начале is perfectly natural and slightly more literary in feel.

Russian past tense agrees with the subject in gender and number.

Here the subject is то:

• то is neuter singular
• so the verb is показалось (neuter singular past)

Compare:

• он показался странным = he seemed strange
• она показалась странной = she seemed strange
• это показалось странным = it seemed strange

In your sentence, the core structure is:

• то показалось мне странным

So показалось matches то.

Мне is the dative case of я.

The verb казаться / показаться normally works with the person in the dative:

• мне кажется = it seems to me
• ему кажется = it seems to him
• нам показалось = it seemed to us

So:

• показалось мне странным = seemed strange to me

This is a standard pattern in Russian:

• Это кажется мне важным. = This seems important to me.
• Она показалась ему усталой. = She seemed tired to him.

Because after казаться / показаться, the word describing what something seems like is very often put in the instrumental case.

So:

• казаться странным = to seem strange
• казаться важным = to seem important
• казаться правильным = to seem correct

That is why we get:

• показалось мне странным

Here странным is the instrumental singular form of странный.

A useful contrast:

• Это странно. = This is strange.
  Here странно is a short-form adverb/predicative word.

• Это кажется странным. = This seems strange.
  Here странным is instrumental after кажется.

So in your sentence, странным is exactly what Russian normally uses with показалось.

This is a very common Russian possession pattern:

• у + genitive + быть

Literally, it is something like at someone there was..., but in natural English it usually means someone had...

So:

• у свидетельницы было... лицо = the witness had... a face / expression

Russian strongly prefers this construction in many everyday situations, especially with:

• physical features
• body parts
• states
• things someone has with them

Examples:

• У него были голубые глаза. = He had blue eyes.
• У неё был спокойный голос. = She had a calm voice.
• У ребёнка была температура. = The child had a fever.

Using иметь is possible in Russian, but it is often more formal, bookish, or less natural in these contexts. With body parts or facial expression, у кого-то было... sounds much more idiomatic.

Yes, свидетельница is specifically a female witness.

In the sentence you see свидетельницы because after у, Russian uses the genitive case:

• nominative: свидетельница
• genitive: свидетельницы

So:

• у свидетельницы = of the female witness / the female witness had

Compare:

• свидетель = witness, usually male or sometimes general
• свидетельница = female witness

So the sentence clearly refers to a woman.

Because in the construction у кого-то было что-то, the thing possessed is the grammatical subject of было.

So:

• у свидетельницы было лицо
• лицо is nominative singular
• спокойное agrees with лицо in nominative neuter singular

That is why we get:

• слишком спокойное лицо

not instrumental.

You can think of the structure like this:

• [У свидетельницы] [было] [слишком спокойное лицо].

The descriptive adjective stays with лицо and matches it.

The colon introduces an explanation of the previous idea.

The first part says:

• Теперь я понимаю то, что в начале показалось мне странным

Then the colon tells you: here is what that strange thing was:

• у свидетельницы было слишком спокойное лицо

So the colon works like namely / that is / specifically.

In English, we often do the same:

• Now I understand what seemed strange to me at first: the witness’s face was too calm.

So the punctuation is not random; it marks the second part as an explanation or clarification of the first.