Yes, “all” and “both” can both be translated into “都 (dōu)”in Mandarin Chinese. In Chinese sentence, “都” is always put after the subject and before the predicate.
Look at the examples you mentioned:
Tāmen dōu xǐhuān liúxíng yīnyuè.
他们都喜欢流行音乐。
Both of them like pop music.
In the sentence above, “都” is put after the subject “我们” and before the predicate “喜欢.”
Shàng zhōumò wǒmen dōu qù kàn diǎnyǐng le.
上周末我们都去看电影了。
All of us went to see the film last weekend.
In the sentence above, “都” is put after the subject “我们” and before the predicate “去.”