The British royal family doesn't effectively rule over anything. They remain the head of state of some Commonwealth countries (Canada and the UK for example) but not others (India for example).

The Magna Carta (1215) was part of the the beginning of a process that stripped the royals of their power, but it was an extremely long process. I'm not sure when to date the time at which the royals no longer had any practical power, but the broad range would likely be within the 50 or so years prior to WW1. The royals probably still had some influence on public policy past WW2, but not power.

I'm not sure what you mean by "who owns the money". People in Commonwealth countries own their own money. If you mean government money, there is a legal fiction called the "Crown" which owns the money, in the same way that you might say "The People" own money that the US government has, but it's not like individual people could go take their share out. The "Crown" is legally distinct for each commonwealth realm, and even within individual commonwealth realms, for example in Canada several provincial governments are suing the federal government right now over whether the feds have the authority to impose a particular tax. It's the "Crown" of each jurisdiction that's a party to this case, although it has nothing to do with any individual member of the British royal family and I doubt any of them are even aware of the controversy and the lawsuits.