That's an intimidating wall of tables. Any same person would run screaming. I prefer these rules: http://www.nthuleen.com/teach/grammar/adjektivendungenexpl.html (they're still complex, but learnable).
Thanks. It says chiefly British but since there are no Brits kicking up a fuss, I'm guessing it must not be common.
You are right, it is very uncommon in Britain, and I suspect most Brits (I am one) would never use it, or believe it was a misspelling. Only common use I can think of is the specialised one used of mainly nonconformist church groupings. We talk of the Methodist Connexion
Why is "relationships" not acceptable? That's how Verbindung was introduced in a previous lesson. Other language learning websites (memrise) define Verbindung in a dating/marriage context. So which is it? Because I wouldn't refer to a dating couple by saying "They're in a connection".