I think people can run full node even without Bitcoin Core?
The protocol is open source, so someone could make their own node. But I'm pretty sure Bitcoin Core is the standard.Quote
Is that warning not pertaining to Bitcoin Core but to bitcoin generally?
Define "Bitcoin" 
My interpretation is that "Bitcoin" is whatever Bitcoin Core says it is. Until the community agrees on a change.Quote
With how bitcoin is today, it is better than the software the banks are using in term of security of your coins.
I'd argue the entire "euro" project should be called experimental 