Can I drink coffee and tea, or will the caffeine dehydrate me?

Yes. Both can even count towards your daily fluid goal, just remember to also consistently drink other fluids throughout the day. Drinking coffee and tea are both net hydrating meaning that you will still gain hydration from drinking them. Caffeine is a mild diuretic, but should not leave you in a state of being dehydrated. Be sure to not consume caffeinated beverages too late, however, as this will negatively influence your sleep quality.