In other exercises, "modern" is often translated as "fashionable", which is also in the dropdown list. Here it is considered wrong. Is that simply because a "fashionable building" seems like a weird concept or is the meaning just different depending on the context in which it is used?
I think the primary meaning of "modern" is"modern", but it can also mean that it's trendy if you talk about clothes or something. Here it's just obvious that it's not this second meaning.
By the way, what shows the dropdown list has nothing to do with the sentence, every word has the same dropdown list of all possible meanings on every sentence where it appears. That's just how Duolingo work, so don't always trust this list, act as if it's not there unless you really forgot what the word means.
As a reply on a question both works but in other situations "med" and "också" have different meanings. "Med" means with and "också" means also. The english trabskations to the swedish versions of me too is "also me" for jag också and "me with" ( like a command to also be included ) for jag med.