At the start of the play, is Elyot in love with Sibyl? How can the reader tell?

No. Sibyl demonstrates early on that she is very naive and inexperienced, not to mention insecure and in need of constant reassurance. From the start, however, Elyot is witty and intelligent, though detached from his new wife. He grows annoyed with Sibyl's habit of bringing up Amanda every chance she has in order to hear Elyot say negative things about her. He seems incredulous by Sibyl's lack of spirit (for example, his reaction to Sibyl's announcement that she will not get sunburned).