Ich markiere die Antwort mit einem Kreuz.

Markiere is the 1st person singular present tense form of the verb markieren (to mark).

The pattern is:

• ich markiere = I mark
• du markierst = you mark
• er/sie/es markiert = he/she/it marks

So ich markiere is the correct form for I mark.

Antwort is a feminine noun in German: die Antwort.

That is why the sentence says:

• die Antwort = the answer

If you changed the noun, the article would change too:

• der Text = the text
• das Wort = the word

Here, Antwort is also the direct object of the verb markiere, and in this case the feminine article stays die in both nominative and accusative:

• nominative: die Antwort
• accusative: die Antwort

So the form does not change here.

Because the preposition mit always takes the dative case.

So:

• ein Kreuz = a cross/X marking form in nominative or accusative
• mit einem Kreuz = with a cross / with an X mark, after mit

Kreuz is a neuter noun (das Kreuz), and the dative singular of ein with a neuter noun is einem.

So:

• das Kreuz
• ein Kreuz
• mit einem Kreuz

It is dative.

You know this because of the preposition mit, which is one of the German prepositions that always requires the dative.

So in the phrase:

• mit einem Kreuz

the whole phrase is a dative prepositional phrase meaning with a cross / with an X.

A useful rule to remember:

• mit + dative

Examples:

• mit dem Stift = with the pen
• mit einer Freundin = with a female friend
• mit einem Kreuz = with a cross / with an X

Not necessarily. In this sentence, Kreuz usually means a cross mark, often an X used to mark an answer on a form or test.

So mit einem Kreuz often means something like:

• with an X
• by putting a cross next to it
• using a check-mark style mark, depending on context

Yes, Kreuz can also mean cross in the religious or shape sense, but here the context is clearly about marking an answer.

This is normal German main clause word order:

• Ich = subject
• markiere = verb
• die Antwort = direct object
• mit einem Kreuz = prepositional phrase

German main clauses usually put the conjugated verb in second position:

• Ich markiere ...
• Heute markiere ich ...
• Die Antwort markiere ich ...

So the sentence follows the standard pattern very naturally.

Yes, depending on context, that can also be natural.

There is a slight difference:

• Ich markiere die Antwort mit einem Kreuz.
  = I mark the answer with a cross/X.

• Ich kreuze die Antwort an.
  = I tick/check/select the answer.

The second one uses the separable verb ankreuzen, which is very common for forms, tests, and multiple-choice questions.

So if you are specifically choosing an answer on a questionnaire or test, ankreuzen is often the more idiomatic verb.

Because all nouns are capitalized in German.

So:

• ich is not capitalized here because it is a pronoun, not a noun
• Antwort is capitalized because it is a noun
• Kreuz is capitalized because it is a noun

This is one of the most noticeable spelling rules in German.

A rough English-friendly guide would be:

ikh mar-KEE-ruh dee ANT-vort mit EYE-nem kroyts

A few pronunciation notes:

• ich: the ch is a soft sound, not like English k or sh
• markiere: stress is on -kie-
• die sounds like dee
• Antwort is pronounced roughly AHNT-vort
• einem is roughly EYE-nem
• Kreuz rhymes roughly with English voice if you replace the beginning with kr-

Not exactly.

• Kreuz usually suggests an X-shaped mark
• Häkchen usually means a check mark / tick

In English, people sometimes blur these, but in German they can describe different symbols.

So:

• mit einem Kreuz = with an X
• mit einem Häkchen = with a tick/check mark

Which one is correct depends on what symbol is actually being used.