With the sentence you quoted, the easiest answer would be to replace the first "and" with a full stop and start a new sentence:
Your version: I'm a great fan of your novels and am also planning to write my first science fiction and when it's finished I might seek publishing. I know you'd think this is a silly idea but I really want to give it a try.
Revised: I'm a great fan of your novels. I'm also planning to write my first sci-fi and when it's finished, I might seek to have it published.
With spoken English, especially with examples from You Tube or interviews, the word "and" is used more often, simply because people don't necessarily plan what they're going say in advance. As we speak, we think of more things to say so we will frequently say "and" because we've thought of something else that we want to add, and don't necessarily finish the original sentence first.
Student or Learner