First notebook entry: Introducing myself

I like to listening to music and spending time with friends.
I teach am learning English because in the future I want to travel the world!

Notes:

1. You don't really need "in the future" because that is clear from the context.

2. In general, don't use a comma before 'because".

First notebook entry: Introducing myself

I like to listening to music, spending time with friends.
I teach English, because in the future I want to travel the world.

Your first sentence,yo do not need to use to twice.Just I like to listening music,because listening is gerund and it is a noun,music too.

First notebook entry: Introducing myself

I like to listening to music, spending time with friends.
I learn English, because in the future I want to travel the world.

First notebook entry: Introducing myself

I like to listen to music and to spend time with friends.
I teach English, because in the future I want to travel the world.

Do you teach (преподавать) or learn/study (учить/изучать) English?