1. Parque Lage is a public park located in the Jardim Botânico neighborhood in Rio de Janeiro, Brazil. It is known for its beautiful gardens, historic mansion and stunning views of the city and the Corcovado mountain. The mansion was built in the early 20th century and was used as a private residence before being acquired by the Brazilian government and turned into a public park in 1961. It has since become a popular spot for locals and tourists alike, offering a range of activities such as hiking, picnicking, and visiting art exhibits. The park is also frequently used as a film location, with scenes from movies such as \"The Incredible Hulk\" and \"City of God\" being shot there.

2. Parque Lage is open daily from 8am to 5pm. Their phone number is +55 21 3257-1800.

3. Admission to the park is free. As for transportation, visitors can take a taxi or use public transportation such as buses or the subway. The nearest subway station is Botanic Garden (Jardim Botânico). It is also possible to hike to the park from the Corcovado mountain.