Firefox is not trusty. Having your email and calendar on Google is not a risk as long as you sync them so if something happens to your accounts that you can move them to another provider.
Having your email on Google is not a risk
If you're a company and don't want to manually handle email provisioning? Sure, why not. If you're an individual, Google isn't great. You could have a decent feature set along with great customer support elsewhere.
No, that’s not true. In the case where google shuts down your email, you will lose every email sent to that account after the shut down, and you’ll need to find everything and everyone that might send email to youraccount@gmail.com. This is why having a separate domain is super important, you could switch the MX records with minimal interruption.