Taky tě mám rád.
What is the difference between this and 'mám rád tebe'?
Mám rád tebe. stresses that you like this person and not some other person, which someone probably thought you like instead.
This sentence is spoken by a female speaker. Would then not "Mám tě ráda" be correct?
In the English-to-Czech reverse exercise, "Mám tě ráda" is accepted, since gender is not clear. But, FWIW, the TTS uses a female voice throughout the course.
The voice is just a female narrator pronouncing some sentences, it does not mean the sentences were originally uttered or written by a female person.