Страхователь заявил об ущербе сегодня.

Страхователь means the policyholder or the person/company that takes out the insurance policy. It is not the insurance company itself. The insurance company is страховщик.

Grammatically, страхователь is in the nominative singular, because it is the subject of the sentence.

Заявить is the infinitive: to declare / to report.

Заявил is the past tense, masculine singular form: reported / declared.

So:

• заявить = to report
• заявил = he reported / the policyholder reported

Russian past tense forms change for gender and number, so here the sentence needs a past-tense form, not the infinitive.

This is a question of aspect.

• заявить → perfective
• заявлять → imperfective

In the sentence, заявил presents the action as completed: the policyholder made the report today.

If you used заявлял, it would sound more like:

• he was reporting,
• he used to report,
• he reported repeatedly,
• or the action is being described without focusing on its completion.

For a single completed act today, заявил is the natural choice.

Because the verb here uses the pattern заявить о чём-то = to report / declare about something.

So the structure is:

заявить + о/об + Prepositional case

You get:

• о договоре
• о проблеме
• об ущербе

The form об is used instead of о before a word that begins with a vowel sound, like ущербе.

So:

• о
  • consonant-starting word
• об
  • vowel-starting word

Because after о / об, Russian normally uses the prepositional case.

The dictionary form is:

• ущерб = damage, loss

After об, it becomes:

• об ущербе

That -е ending shows the prepositional singular.

So this is the same kind of change as:

• дом → о доме
• договор → о договоре
• ущерб → об ущербе

In the Russian past tense, the verb agrees with the subject in gender and number if the subject is singular.

Here the subject is страхователь, which is a masculine singular noun, so the verb is:

• заявил = masculine singular

Compare:

• страхователь заявил = the policyholder reported
• страховательница заявила = the female policyholder reported
• страхователи заявили = the policyholders reported

Yes, it can go elsewhere. Russian word order is much more flexible than English word order.

This version is neutral and natural:

• Страхователь заявил об ущербе сегодня.

But you could also say:

• Сегодня страхователь заявил об ущербе.
• Страхователь сегодня заявил об ущербе.

The basic meaning stays the same, but the emphasis changes slightly:

• Сегодня at the beginning highlights today
• сегодня later in the sentence sounds more neutral or less emphasized

Normally, in this meaning, no. The standard pattern is заявить о чём-то.

So:

• заявил об ущербе = reported damage / made a report about the damage

If you use заявить with a direct object, it usually means to state, declare, announce something:

• заявить протест
• заявить позицию
• заявить требование

So in this sentence, об is not optional; it is part of the normal construction.

Because Russian has no articles. There is no direct equivalent of the or a/an.

So Страхователь заявил об ущербе сегодня can mean:

• The policyholder reported the damage today
• or, depending on context, A policyholder reported damage today

Russian leaves that kind of definiteness to context rather than marking it with an article.