Translation:František is buying a house in that city.
Native English here— "Frantisek buys a house in the city" feels like the correct translation to me, and even though it's present simple, he doesn't need to be doing so repeatedly.
Yes, it's used here. Normally, every time you have "Someone is doing something" the "something" is in the accusative (unless another case is specifically required by the verb, for example). This "is doing" can be pretty much any verb, including "mít" (to have), but it doesn't apply to simple "být" (to be).
Here, "dům" has the same form in the accusative as in the nominative. This is true for all masculine inanimate and neuter nouns, and for feminine nouns that end in a consonant. You will have to (gradually) learn the various forms of nouns in all cases.
- Stůl (table, masculine inanimate) -> Kupuje stůl. (He's buying a table)
- Pivo (beer, neuter) -> Má rád pivo. (He likes beer)
- Voda (water, feminine) -> Pije vodu. (He's drinking water)
- Kluk (boy, masculine animate) -> Vidí kluka. (He sees a boy)
In all the above sentences, the nouns are in accusative, but sometimes (stůl, pivo) they look the same as nominative.