you will be fine in your situation. Nothing to be concerned about. Why would you be having second thoughts? Don't listen to the Facebook chatter. I've lived here for 28 years and I've never felt that I am unwanted here.
yes the account used for immigration purposes is the exception which is why a will is the best route to go. I even have joint accounts listed in my will even though there is only one signature required to access it. You might as well list all of them on a will whether they are sole or joint accounts.