Yeah...that's what I would say as well.
But I guess the team has made a decision that a Finnish-style pulla just doesn't exist in the English speaking world in the same sense, and therefore it gets to keep its name, just like sisu and mämmi (but not pesäpallo, which is translated as nestball or something).
Keeping the word "pulla" makes sense, as food items often keep their original name in English if there is no perfect equivalent. A croissant is a croissant, not a bun, a chorizo is not called a "spicy red sausage", a tortilla is not called a "thin flat bread" and a crème brûlée is not called a burnt cream either.
I feel like there is no satisfying translation for neither pulla nor mämmi. Since every translation you try is not really correct.
Just take your "bun" suggestion. It is kind of the same, but also it's not. Typical example of "same same but different". Just do an Google image search for bun. I wouldn't call those things pulla. Maybe "pulla like". If you told someone: I am eating a bun, they wouldn't think of a typical pulla.
It would be like calling pesäpallo just baseball. It's kind of similar but definitely not the same thing. If I told someone (even another Finn): I am playing baseball. He or she does not think of pesäpallo. I would say: I am playing a baseball like game. So the person wouldn't confuse it with baseball.
Anyhow: country specific food or sports, which are not really widespread outside the borders are difficult to translate. So I am quite fine with the decision to just call pulla a pulla
Do they bake? Pullataikina is a pretty specific dough, which of course you can then make many different things out of (even bilberry pie -- the disagreement about the correct dough to use for bilberry pie is almost as serious as the one about the correct filling of laskiaispulla).
The problem with the word bun is that that can also be a savory baked good, which pulla never is.
this translation sounds off. Duolingo, I think you need to make up your minds whether to include an article or use a plural. you can talk about: tea and a biscuit - yup tea and biscuits - fine tea and biscuit - nope. just does not work. I don't see why pulla should be treated any differently... ??
About the second serving…
The whole question concerns regular coffees, no expresso, latte etc.
In Sweden a second serving of coffee is very often included, gratis,. The phrase you see in signs there is Påtår ingår.
In Finland the situation varies. The most common model seems to be that you get a second serving at a highly reduced price, say 0,50 €. The phrase used for advertising this varies: lisäkuppi (standard) or santsi(kuppi) (coll., ← [de] Schanze) are the most common ones. There can also be big dialectal variations. For instance I would say in my home town Ei påtår hinta kuulu?, but I know that I might not be understood in other parts of the country.