Learn Spanish (Spain): Tengo una llamada de mi jefe.

In Spanish, the verb itself tells you who is doing the action. Because tengo only ever means "I have", adding the pronoun yo is unnecessary unless you want to emphasize that it is you who has the call.

Is llamada related to the verb llamar?

Yes! Llamada is a feminine noun meaning a call, and it comes directly from the verb llamar (to call). You will often see Spanish nouns built from verbs like this.

Does de mean "from" or "of" in this sentence?

It means "from" here. The preposition de is very versatile in Spanish. It can mean "of" to show possession, but it is also used to mean "from" to show the origin of something, like a phone call.

How would this sentence change if my boss were a woman?

You would change jefe to jefa. The Spanish word for boss changes to match the person's gender, so a female boss is mi jefa.