I keep getting emails from apple saying to update my account details

I have received repeated emails this week saying I need to update my account details and they have case I’d number on them. I didn’t use any links in these emails to sign into my account. I do not have a current credit card entered and didn’t plan on entering one as. Have not been making purchases and didn’t feel I’d have a problem if it refused me a purchase and I’d enter it then. Secondly I thought I’d change my id which is my email address and it won’t let me. Now I’m logged in and when I hit edit to change that information it says my session has timed out. I just signed in two minutes ago and it keeps taking me in circles. Getting very frustrated. Plus when I log in I get in but it asks for a six digit code and up pops the code. How secure is it when the code shows up on the same screen. Should it not arrive via email?.. and of course trying to find a contact number. Not happening. Just about had it