How to fix the first line?

Also known as or aka would refer to an alias, not a description of their different works.

Cressida Dick is the head of the metropolitan police, she is not also known as the head of the metropolitan police.

I would say, “Mark Lee Kok Huang is a famous Singaporean comedian.....”

Is he famous outside of Singapore? I’ve not heard of him, but that doesn’t mean much. If he isn’t well known outside of Singapore I would change famous to popular.

Mark Lee Kok Huang, the Singaporean comedian, actor, television host and film director, has announced that he is stepping away from the entertainment industry completely to focus on his new career path.

- FIXED.