If a word or sentence is used many times on a page, can I somehow code the extension so that this word/sentence only needs to be translated once?
Topic on Help talk:Extension:Translate
No. If that word or sentence is an independent unit, you can use the translation memory to speed up the translation.
You mean, if a user has to translate the same word three times, the system suggests the first translation when translating the second occurance if the word?
(In my template, the line "Photo:" has to be translated four times.)
Yes, you need to translate it four times, but you can pick up the translation from the translation memory. The translation memory works on the unit level, so it does not suggest translation for words embedded in a sentence.