We have carried out an intensive study of photometric (Kepler Mission) and spectroscopic data on the system Kepler-2 (HAT-P-7A) using the dedicated software WinFitter 6.4. The mean individual data-point error of the normalized flux values for this system is 0.00015, leading to the model's specification for the mean reference flux to an accuracy of similar to 0.5 ppm. This testifies to the remarkably high accuracy of the binned data-set, derived from over 1.8 million individual observations. Spectroscopic data are reported with the similarly high-accuracy radial velocity amplitude measure of similar to 2 m s(-1). The analysis includes discussion of the fitting quality and model adequacy. Our derived absolute parameters for Kepler-2 are as follows: Mp (Jupiter) 1.80 +/- 0.13; R1.46 +/- 0.08x106 km; Rp km. These values imply somewhat larger and less condensed bodies than previously catalogued, but within reasonable error estimates of such literature parameters. We find also tidal, reflection and Doppler effect parameters, showing that the optimal model specification differs slightly from a 'cleaned' model that reduces the standard deviation of the similar to 3600 binned light curve points to less than 0.9 ppm. We consider these slight differences, making comparisons with the hot-Jupiter systems Kepler-1 (TrES-2) and 13. We confirm that the star's rotation axis must be shifted towards the line of sight, though how closely depends on what rotation velocity is adopted for the star. From joint analysis of the spectroscopic and photometric data we find an equatorial rotation speed of 11 +/- 3 km s(-1). A slightly brighter region of the photosphere that distorts the transit shape can be interpreted as an indication of the gravity effect at the rotation pole; however we note that the geometry for this does not match the spectroscopic result. We discuss this difference, rejecting the possibility that a real shift in the position of the rotation axis in the few years between the spectroscopic and photometric data-collection times.Alternative explanations are considered, but we conclude that renewed detailed observations are required to help settle these questions.