When the Gaia parallax data (especially for Cepheid stars) become accessible to public? If it is already released for some parts, where can I find it?
Gaia data release 1 was announced in September 2016. It has parallaxes for 2 million stars previously observed by the Hipparcos mission, a small fraction of the 1.1 billion positions recorded so far. Future releases will of course have more data and smaller errors.
Gaia has ~600 light curves for Cepheids but probably not parallaxes for most of those. Casertano et al. 2016 checked Gaia parallax data of some Cepheids against expected values from ground-based photometry.