Difference between kummern, betreuen, and durchfuhren ? they all mean "to take care", right ? thanks

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Ich kuemmere mich um meine kleine Schwester. That is more general, taking care of your sister.
Ich betreue Eine behinderte Frau. That is more professional, like a job.
I am not sure about the last word. durchfuhren is the past tense of driving through, e.g. a tunnel. the verb durchfuehren means something like to execute a task.

Answer

These words are different enough that you will find the answer to your question in any decent dictionary - even in your native language instead of English. Here are some suggestions:

https://dict.leo.org/französisch-deutsch/
https://fr.pons.com/traduction
https://glosbe.com/de/fr

And since you are a professional teacher yourself: How important is the correct usage of diacritics (accents, cédille, ...) for you? There is a huge difference between "durchfuhren" and "durchführen", and "kummern" is not a word in German (but "kümmern" is). If you really can't type the German ä/ö/ü, please replace them by ae/oe/ue. On the other hand, it's not really impossible, if you put at least a little bit of effort into it. See this discussion thread: https://www.italki.com/discussion/184578