It does, "по-русский" would be I guess a common example and I think "её" can be written just as "ее". I think I've also seen "оо" within one word (I don't remember what it was) and that was weird, it was pronounced like "ao" but for whatever reason written like that.
You're at a pretty high level for a "very limited" vocabulary!
The first one is two voiced s's, the other one is "tsts".
It's a good question why they have chosen to write it like that, since it's pronounced simply as "питса". Actually pronouncing the two 'ц's would be interesting, although I wouldn't be surprised if the equivalent of that existed in some word!
There are three Russian conjunctions that correspond to only two English ones: "а", "но", "и" in Russian versus "but" and "and" in English. So obviously they don't match one to one.
"Но" mean "but" when the second part of the comparison is sort of substracted from the first one. So we'd expect that if A is true, then B has to be true too, but it turns out it's not:
- "Это пицца, но не та, которую я просила" - This is pizza, but not the one I asked for.
"И" means "and" when you add two (or more) things stressing the relations between them:
- "Это пицца и она очень вкусная" - This is a pizza and it's very tasty.
"А" is a tricky one, because it takes some properties of "and" and some of "but", so the translation depends on the context. Mostly it's used to contrast two things:
"Я заказала пюре, а ты заказал пиццу" - "I have mashed potatoes and/but you have pizza" (two different people ordered two different dishes, so there's a contrast and it can't be "и". But there's no implication that we were supposed to order the same thing, so it's not "но" either)
"Это пюре, а не пицца" - This is mashed potatoes (and) not pizza.
"Это не пюре, а пицца" - This isn't mashed potatoes but pizza.
(Note, how in the last two examples Russian uses the same conjunction whereas English uses different ones. Russian focuses on the contrast itself, and it doesn't matter whether the statement is positive or negative)
Generally you can say that "а" means "but" as "rather" and "and" as "whereas".
In Duo's example there is a contrast between what we have "here" (one place) and what we have "here" (another place). However you can say "Это пюре, и вот пицца." as well. It would just imply adding pizza to the mashed potatoes rather than offering a choice between them.
That's the general idea, but there are more nuances in actual usage, of course.