Meine Krankenkasse hat mir erklärt, welches Fieberthermometer für Kinder gut ist.

Because Krankenkasse is a feminine noun in German: die Krankenkasse.

So in the nominative singular, my becomes:

• mein for masculine or neuter nouns
• meine for feminine nouns and plural nouns

Examples:

• mein Hund = my dog
• mein Auto = my car
• meine Krankenkasse = my health insurance company / health insurer

The ending -e shows agreement with the feminine noun.

Krankenkasse usually means a health insurance provider or health insurance fund, especially in the German healthcare system.

It is made up of:

• krank = sick / ill
• Kasse = fund, register, cash desk, insurance fund in this kind of context

A native English speaker might expect something closer to health insurance, but German often uses Krankenkasse to mean the actual insurer or insurance fund, not just the abstract concept of insurance.

Hat erklärt is the Perfekt form: the German present perfect.

Structure:

• hat = auxiliary verb from haben
• erklärt = past participle of erklären

So:

• Meine Krankenkasse hat mir erklärt ...
  = My health insurer explained to me ...

In everyday spoken German, the Perfekt is very common for past events. In written or more literary style, you might also see:

• Meine Krankenkasse erklärte mir ...

Both are grammatically correct, but hat erklärt sounds more natural in normal conversation.

Because erklären often takes:

• a dative person = the person receiving the explanation
• an accusative thing or clause = what is being explained

So in this sentence:

• mir = to me (dative)
• welches Fieberthermometer für Kinder gut ist = what was explained

Compare:

• Sie erklärt mir die Regel. = She explains the rule to me.
• Sie erklärt mich would be wrong in this meaning.

So mir is used because the sentence means explained to me.

Because welches Fieberthermometer für Kinder gut ist is a subordinate clause.

In German, the conjugated verb usually goes to the end of a subordinate clause.

Main clause:

• Meine Krankenkasse hat mir erklärt ...

Subordinate clause:

• ..., welches Fieberthermometer für Kinder gut ist.

That final ist is completely normal in German subordinate clauses.

You can compare:

• Ich weiß, dass er kommt. = I know that he is coming.
• Sie sagt, welches Thermometer gut ist. = She says which thermometer is good.

Here welches means which and introduces an indirect question.

So the clause means something like:

• which thermometer is good for children

This is not a direct question like:

• Welches Fieberthermometer ist für Kinder gut?

Instead, it is embedded inside a bigger sentence:

• Meine Krankenkasse hat mir erklärt, welches Fieberthermometer für Kinder gut ist.

Because Fieberthermometer is neuter (das Fieberthermometer), the form is welches.

Because Fieberthermometer is a neuter singular noun:

• das Fieberthermometer

The question word/determiner has to agree with the noun in gender, number, and case.

Here it is nominative neuter singular, so the correct form is:

• welches Fieberthermometer

Compare:

• welcher Hund = which dog (masculine)
• welche Tasche = which bag (feminine)
• welches Thermometer = which thermometer (neuter)

It is in the nominative.

Why? Because inside the subordinate clause, Fieberthermometer is the subject of ist:

• welches Fieberthermometer ... gut ist

The thermometer is the thing that is good, so it is the subject, and subjects are in the nominative case.

The preposition für always takes the accusative case.

So:

• für Kinder = for children

Here Kinder is plural. In the plural, many nouns already have the same form in nominative and accusative, so there is no visible change:

• nominative plural: Kinder
• accusative plural: Kinder

If there were an article, you would see the accusative more clearly:

• für die Kinder = for the children

Because the subject is singular:

• welches Fieberthermometer = which thermometer

That is one thermometer, so the verb must also be singular:

• ist

If it were plural, then you would use sind:

• welche Fieberthermometer für Kinder gut sind
  = which thermometers are good for children

This follows normal German main clause word order: the conjugated verb is in second position.

So the structure is:

1. Meine Krankenkasse = first element
2. hat = conjugated verb in second position
3. mir = other sentence element
4. erklärt = past participle at the end of the verbal part

German does not count individual words here, but sentence elements or chunks.
So Meine Krankenkasse is one unit in first position, and hat is still correctly in second position.

Yes. The indirect question:

• ..., welches Fieberthermometer für Kinder gut ist.

corresponds to the direct question:

• Welches Fieberthermometer ist für Kinder gut?

Notice the difference in word order:

• Direct question: verb comes earlier
  Welches Fieberthermometer ist für Kinder gut?
• Indirect question: verb goes to the end
  ..., welches Fieberthermometer für Kinder gut ist.

That is a very common German pattern.

Yes, it works well. Erklären means to explain.

This sentence suggests that the health insurer did more than just tell the speaker a name; they explained or clarified which thermometer is suitable.

Other possible verbs would slightly change the meaning:

• gesagt = said / told
• empfohlen = recommended
• mitgeteilt = informed

So:

• hat mir erklärt = explained to me
• hat mir empfohlen = recommended to me

The original sentence sounds natural if the insurer gave some guidance or reasoning.

Yes. Fieberthermometer is a normal German compound noun:

• Fieber = fever
• Thermometer = thermometer

Together:

• Fieberthermometer = fever thermometer / thermometer for taking body temperature

German forms compound nouns very freely, and this is extremely common. English often uses separate words where German uses one long noun.

Other examples:

• Krankenhaus = hospital
• Kinderarzt = pediatrician
• Zahnbürste = toothbrush

So Fieberthermometer is a good example of a standard German compound noun.