Jenny Lind was introduced as the daughter of the teacher Axel Lind. However her father's name was Nils Jonan Lind and his occupation is not clear, as in different sources he is credited as an accountant, in some as a manufacturer.
Jenny Lind's father explained her that her luck is not the theater. The meeting with Andersen would set the scene in 1843. At that time Lind was already a studied actress since 1830 at the Royal Theater Stockholm and became an actress there in 1837. So it shouldn't have been a surprise for his father. And therefore it is very unlikely that Andersen wanted her to study acting.
Andersen's story "Agnete and the Merman" was released in 1833, 10 years before Andersen and Lind met.
When sitting with children and their toy soldiers Andersen suddenly gets inspired about "The Steadfast Tin Soldier". This fairy-tale was released in 1838, 5 years before Andersen and Lind met the first time.
Early in the movie Hans Christian Andersen says that he always dreamed of visiting Italy. The real Andersen actually visited Italy in the 1820s, long before he met Jenny Lind the first time.