The well-known "Casa Azul de Coyoacán" is the place where Frida Kahlo was born and lived her whole life. This house is in Coyoacán, Mexico. So first question is false, because Coyoacán is the south of Mexico, and not in the centre.
Four years after the death of Frida (1954) and one year after the death of Diego Rivera (1957), that is, in 1958, and following the will of the artists, the house became a Museum that was open to all people that wanted to visit. Therefore, second question is true.
Frida Kahlo and Diego Rivera were married and lived together in the house of Coyoacán. Then, the third question is false, because Frida did not lived alone in that house.
Some works of art are seen in the house. Some of them are permanent display "El retrato de mi padre Guillermo Kahlo", "Naturaleza muerta", etc. But the painting "Las dos Fridas" is not there, instead, this work of art is in the Museum of Modern Art in Mexico. Therefore, the fourth question is false.
Frida and Diego first had the house and then purchased the garden, which was designed by Humberto Spindola, a friend of the artists. He is still the gardener of the Museum of Frida. So, the fifth question is false.
The Museum of Frida Kahlo, as today it is known, exhibits several belongings of both artists, such as the wheelchair and the beds of Frida (for she had polio and also had an accident that affected her spine), so the sixth question is true.