Learn Portuguese (Portugal): Eu estou constipado e tenho de descansar.

No, it's a famous "false friend"! In Portuguese, estar constipado means to have a common cold. In English you say "I have a cold", but in Portuguese you are literally saying "I am cold-ed".

Why use estou (I am) instead of sou?

Having a cold is a temporary condition, not a permanent part of who you are. Because of this, we use estou (from the verb estar, which is used for temporary states) rather than sou (from the verb ser, which is for permanent traits).

If a woman is speaking, does any part of this sentence change?

Yes. The word constipado acts as an adjective describing the speaker. Adjectives must match the gender of the person they describe, so a woman would say Eu estou constipada.

Why is there a de between tenho and descansar?

This is how you express obligation ("have to") in Portuguese. The verb ter by itself means "to have" in the sense of owning something. But when you use ter + de + an action verb in its basic form (like descansar), it means "to have to do something".