Repotting, a good first move since every azalea I've ever purchased has been VERY pot bound and often showed some of the symptoms yours is. From what I can tell from your pics, your plant may be suffering from a mild lack of iron from being pot bound. To correct use an azalea/rhododendron fertilizer. As far as the flowers go, these plants often will put on a great show, buds opening all within a short time and then that means that the flowers die out about the same time.

Thank you Raymond. Do you suggest repotting again? Or was that a comment on your experience?

Repotting again isn't necessary. I was commenting on my experience and observations over the years as far as my answer went.

Judging by the leaves that looks to me like a hardy deciduous azalea rather than a cultivar of Azalea indica and, as such, it isn't suited to indoor growing. Do you have any outdoor space for it? The 'sap' appears to be honeydew, excreted by aphids. I also notice all the leaves are angled towards the window which means it is seeking light. If you can't put it outdoors at least turn it regularly.