Many platforms such as exchanges makes 2FA compulsory. How then do you navigate through it? Secondly, I have used Google 2FA for a long time now and even without Internet in my phone so I don't really understand the part you said its connected to the Internet or am I not reading your comment correctly?
With Google 2FA and some like Authy, you can have your 2FA backup online on the cloud, but the best are offline on a paper (like a book). Recommended 2FA examples are Aegis (Android) and Tofu (iOS). I hope you now understand me clearly.
If you have your 2FA offline, it is better. But what that is most necessary is for it not to be on the same device that you have what you are using it for. But having it offline, it adds to your security.
Changing passwords regularly is also risky; honestly, I have all of my passwords saved in my Google cloud; I realise this is risky, but it's the only way I can remember some of the passwords I use because I use various passwords on different sites. I know the best safe is to purchase an offline password manager book, but I can't find it anywhere. Can it be purchased on the Jumia marketplace? If my primary email is compromised, half of my account is compromised as well, which is why having other security layers such as 2FA is critical.
I do not change password regularly, but it is not risky. If I am not able to access the password offline and I need it to access the service I wanted it for, I use forgot password which has been very helpful, it is better than saving password online. I do not have any password saved online anymore as Google is becoming something else as usual.
I use any book for offline backup.
2FA on exchanges are optional..
It differs from one exchange to another. On some exchanges, you will not be able to withdraw without setup 2FA. It is optional on most exchanges that I have used before.