They have liked the idea of me starting my own business.
I've liked the song since my childhood.
I've been liking the song since my childhood.
Q1) I think sentence (3) is not absolutely correct because it uses the stative verb "like" in progressive form. So, the present perfect tense (sentence (2)) would be used to convey the meaning of sentence (3). Am I right?
Q2) Does sentence (1) suggest they have recently liked the idea (as in "I have done the homework"), or does it suggest they have continuously liked the idea and will continue to like it, the same way as sentence (2)?