If you think about how we often say the time within an hour as "15 past X" and "15 til X," doing the same with days in the month doesn't seem as exotic.

There's that language where they do the 'til' thing with the half-hour.

Yeah, those guys.

Yup, in German "halb sechs" is half past five, whereas in the U.K. "half six" would be half past six. It's quite confusing if you're used to one system and suddenly need to use the other.

Confuses the hell out of my missus and kids (which are all English but speak Norwegian) when I say in sentences in half Norwegian half English. Did he mean "half to" or "half past"...

My missus just shakes her head when I use the phrases such as "fem på halv" as in "five to half" which means 25 minutes past the current hour, or "ti over halv" ("ten past half") as in "twenty to the hour"...

We use the same phrases in German, "fünf vor halb" and "zehn nach halb". It's quite useful, there's a description for every five minute offset to the hour: five/ten to/past the half hour or hour, quarter to/past the hour, and of course the infamous "half to". That's before adding in regional time formats, which mostly require reconstruction of missing words ("viertel sechs" is 5:15, "dreiviertel sechs" (three quarters six") 5:45 in my area)

Regarding your last point there is a nicely named website I'd like to share: http://www.norddeutschelernendieuhrzulesen.de/