Learn Spanish (Latin America): No estoy seguro de la respuesta.

This is an example of a governed preposition. In Spanish, the adjective seguro (when meaning "sure" or "certain") always pairs with the preposition de to introduce what you are sure about. You have to learn the phrase estar seguro de (to be sure of/about) as a fixed unit, rather than trying to directly translate English prepositions like "about."

Why is it estoy seguro and not soy seguro?

The verb you choose changes the meaning of the adjective! Estar seguro describes a state of mind, meaning "to be sure" or "to be certain." If you use ser seguro, it means something is "safe" or "reliable" (like a neighborhood or an investment). Since the speaker is expressing their own lack of certainty, we use estar.

If a female speaker is saying this, does the sentence change?

Yes. Because seguro is an adjective describing the person who is speaking, it must agree with their gender. A female speaker would say No estoy segura de la respuesta.

If I want to say "I am not sure THAT it is the answer", do I keep the de?