Learn Italian: Perché sei preoccupata? Ho troppo stress. - "Why are you worried?" "I have too much stress."

Because the person being spoken to is female. Adjectives in Italian must match the gender of the person they describe, so if you were speaking to a male, you would ask Perché sei preoccupato?.

Is stress a masculine or feminine word?

It is masculine. In Italian, foreign loanwords that end in a consonant (like stress, sport, or bar) are almost always masculine singular. That is why the adjective troppo (too much) ends in -o to match it.

Could perché also mean "because" here?

In Italian, perché means both "why" and "because". Here, the question mark makes it clear it means "why". If the second person had answered Perché ho troppo stress, it would mean "Because I have too much stress."

How would I reply to this person to give them advice?

This is a great place to practice the current lesson! You can use the present conditional of dovere to say "you should", such as Dovresti riposare (You should rest). You could also use potere to say "you could", like Potresti fare una vacanza (You could take a vacation).