Is my Minecraft connected to my Gmail account?

Yes and no.

Your Minecraft account is connected to the email that was used when you registered your account. Which means if you lose your account you would also lose access to your Minecraft and Mojang account.

However while you still have access to your Minecraft account, you can update your email and prevent yourself from being locked out.

If you already missed that, then your last chance is manual reset which can only be done by Minecraft people. Basically you need transaction ID for purchase (your Minecraft account) and they will reset your password and email if needed – but keep in mind this can take time as they’re checking it by hand.