Do you have to learn Erlang to learn Elixir?

No, you can just learn elixir. Learning both can be beneficial, since you can call erlang code from elixir, but you can get very far without learning erlang.

The official Getting Started guide is an excellent starting point

A good Elixir programmer should at least be able to read Erlang code. However that is only needed much later.

No, you do not need to, but sooner or later at least minimal knowledge will be handy. However you will not avoid learning OTP principles.

If you feel interested in learning Erlang but can’t wrap your head around its syntax, I’d reccomend a minimal introduction to Prolog: apart of being an amazing and mind blowing programming language, you’ll find there the origin of many Erlang strangenesses

Sort of. You won’t need to learn the Erlang language. However, there are occasionally things you might want to do, that you’d think might be in the Elixir standard libraries, or at least easily available from some common well-supported hex package. Sometimes you’re right, but sometimes the things aren’t in those places, but are in the Erlang libraries. So, you’ll quite likely need to learn how to find something in the Erlang libraries, and call it from Elixir. (Sorry, my own usage hasn’t been serious/frequent enough that I remember offhand those details, just that they exist.)

I learned Elixir before ever touching any Erlang, but picked up quite a bit of it along the way.