If you keep browsing with the same browser on the same laptop/desktop, the 30 day save will work until it expires or you clean the cookies on your browser whichever comes first. Switching IP addresses will not change the 2-factor verification code already saved on your machine.

As for the phone numbers, you can set which one you would like to receive calls/SMS as primary phone that way you know which phone you should use. You signed up an account with them less than 1 business day ago, so you should wait 2-3 more days to see if a verification transaction shows up on your bank account (in case you chose to have some tiny amounts of funds deposited onto your account, I actually don't know how the verification works if you gave them your account login credentials to instant verify). Verification is required if you want to buy or cash out some bitcoins with your bank account. Sending and receiving BTC are basically free and ready to go as soon as your account is created.

My 2 cents hope that helps.