Learn Spanish (Latin America): Con tener una cola larga, la cometa había caído al suelo. - Despite having a long tail, the kite had fallen to the ground.

Using con followed by an infinitive is a concessive structure that expresses "despite" or "even with". It is a slightly more colloquial alternative to a pesar de tener or aunque tenía. You use the infinitive tener here because the subject (the kite) is the same for both halves of the sentence.

I thought cometa was masculine. Why is it la cometa here?

This is a noun that changes meaning entirely based on its gender. La cometa is feminine when it means "the kite" (the toy you fly on a string). If you use the masculine form el cometa, it means "the comet" (the celestial body in space).

Could I just use cayó instead of había caído?

You could use cayó (the simple past) to state the isolated event: "the kite fell". However, había caído is the past perfect tense (had fallen), which sets the scene. It emphasizes that the kite had already hit the ground before whatever else the speaker is about to mention next in their story.

Why do we say al suelo instead of en el suelo?