"onto" the street or "into" the street, but no one ever just says "to" the street. Reported.
It definitely sounds a little funny. Probably is technically correct. "Onto" or "into" are both better.
I am hearing kabadban instead of kabatban -- is this a case of retrogressive voiced assimilation or am I hearing things?
No, you're not hearing things. [tb] is one of the sound combinations that are rather hard to pronounce, so they blend a bit together and the t gets voiced to "kabádban".
Also, how can "we" all be wearing one coat? Is this a really huge coat? Or are "we" extremely small people? Is this "we" a collection of gnomes?
Should be "in coats" in English, but the Hungarian sentence is correct like this.
with our coats on should be accepted. You need to be more flexible.