Japanese has a wide variety of phrases that show one sentence relates to the last. For lack of a better term, I'm going to call these words Sentence-Initial Conjunctions.
- Demo, equivalent to "however" or "but, which is used when the speaker is giving information that shows a contrast to the previous sentence.
****As it is said that no matter how much good things you complement about someone.....if There is a "BUT", everything goes down to drain......so "BUT is a bit of Poison"***
In the your Examples:
1)He has a scary face but a heart of gold.
Japanese Translation : Kare wa kowai kao o shite iruga, yoi kokoro o motte iru.
As the tone of contrast from the first part of the sentence completely changes after you say "but" likewise the tone of contrast changes after you say "iruga", here "iru" means "has" and in Japanese grammar the word "ga" is attached with the last word of the first part of the sentence as way of differentiating it from the second part of the sentence.
2)She's very quiet but also very direct.
->Translation: Kanojo wa totemo shizukadesuga, mata hijō ni chokusetsutekidesu.
The word "ga" in "Desuga" is the contrasting word here or "BUT".......when you speak the sentence, it will naturally carry the same tone when you speak Japanese fluently.....It will slightly vary a bit because of the Japanese accent.....but the Japanese people will get the tone u are trying to convey.
There is a certain pause of 1 second after the part "She's very quiet" .......then comes the next part "but also very direct". This is the tone we use in English. In case of Japanese.....There is a pause after the syllable "Ga" in the word "Shizukadesuga" which when comparing with English the 1 second pause would be after saying "But" in case of Japanese. But the despite the slight variation in tone, Japanese native speakers will get the contrasting tone like the one we have in English.
3) I was doing my best, and yet I also wanted to give up.
->Translation: Watashi wa saizen o tsukushite itaga, soredemo watashi wa akirametai to omotta.
As you can see here as well, there is "ga" in the word "itaga"......ga is used as a context to contrast between two parts of the same sentence....... and naturally there will always be a pause after it and the contrasting word "soredemo" or ("and still"/"But still") comes later .......like the small gap we have after the word "best"
4) I am very happy yet not satisfied.
->Translation: Watashi wa totemo manzoku shite iruga manzoku shite inai.
Its the same thing here too.......the pause is right after "ga" in the word "iruga" which is "yet" in the sentence.
Note: For most of the contrasting sentence, according to Japanese Grammar we use "ga" for but, yet etc.
Hope this info helped you out.......you can try listening to contrasting sentence in Japanese Audio Books online to help you better understand the tone and the pause in the sentences.