There is nothing wrong with keeping emergency fund and back fund together. But if you keep them together then you may face some problems like if you keep your emergency fund and back fund in the same account then if your account gets locked then in this situation if you face any emergency then you may face some problems.
your explanation here shows that you are very confused in what you are actually saying, and I would suggest that you read more of JJG post to gain more knowledge before engaging in conversation, because knowledge is key to a better conversation and sharing of knowledge.
Emergency fund is money kept for personal or family needs
No, you are wrong here, emergency funds is the money kept aside that stands as the last layer of protection of your Bitcoin holdings, it's the money kept aside to use in sorting out any real life emergencies that may threatens your holdings.
and back fund is money kept for future in any personal or business sector.
while back up fund's is that spare money kept aside with the purpose of backing up your investment, like using it to invest aggressively during a dip or you can use it to for some other stuff that may have warrant you to dip into your emergency funds, but take note that your emergency funds is the last layer of protection of your Bitcoin investment, that's why it's very unwise to use it for anything else, except a real life emergency situation that threatens your bitcoin holdings.