You do not need an account on bitpay.com to use your BitPay Wallet. Your BitPay Wallet is secured using your device and your private key: by design, BitPay never has access to your bitcoin or your wallet.
Have you backed up your BitPay Wallet? It's extremely important that you do so.
If you don't set up a backup and lose your wallet (hard drive failure, theft, etc.), then the funds inside will not be able to be recovered. (Note that this is true for all bitcoin wallets.) See: https://support.bitpay.com/hc/en-us/articles/115003004363-I-lost-my-wallet-or-changed-my-phone-What-can-I-do-to-restore-my-wallet-
You don't need a second device, you just need to copy down the recovery phrase and keep it somewhere safe. Please don't do anything like email it to yourself or keep a copy on the device where your Wallet is. If you do this and then your device is stolen, then the thief would be able to steal your wallet's funds as well.
You can review the Wallet's Terms of Service and all of our help center's articles on the Wallet here.