1) Yes. When we increase V/f, by increasing voltage with the same frequency, flux density will go up as per the transformer equation that I mentioned earlier. If you keep V, input voltage, constant, but reduce the frequency (60 to 50 HZ), then also V/f will go up, increasing flux density.
2) I believe you are supplying a 15 KVA 480 V 60 HZ unit. Designed for 60 Hz but testing at 50 Hz. You propose to extrapolate test results for 60 Hz from 50 Hz measued values. I had done that many times. Earlier days, these conversion factors were not stanbdardised. Thanks to Ramsis Girgis of ABB, St.Louis, these were studied in detail during 2000-2001 and IEEE incorporated these recommendations in latest revision of the standard. You can get more details from below:
a)R. S. Girgis, B. Beaster, and E. G. teNyenhuis, “Proposed standards for frequency conversion factors of transformer performance parameters,” in Proc. IEEE Power Eng. Soc. Transm. Dist. Conf. Expo., vol. 1, Oct. 28–Nov. 2, 2001, pp. 153–158.
b)Ramsis Girgis, and Ed te Nyenhuis, 50 Hz to 60 Hz Conversion factors for transformer performance factors, Presentation at IEEE/PAS Spring 2002 Meeting
c)IEEE Std C57.12.90-2015; IEEE Standard Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformer- Annexure B- 50/60-Hz frequency conversion of measured performance parameters.
d)K R M Nair, Power & Distribution Transformers, Practical Design Guide, Section 30.7, Pages 408-411, CRC Press, 2021
3) Regarding kVA at different frequencies- When a 60 Hz transformer is used in 50 Hz, voltages are reduced by 1.2 to avoid core saturation. Thnen your kVA will be reduced by 1.2 as mentioned by waross. ( when you use a 50 Hz unit in 60 Hz this limitation is not there as B will be coming down at higher frequency) But this is not a must. If your designed B is below 1.4 T, you can use without reducing voltages and the rated kVa will remain the same at both frequencies.