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Sig figs are mainly important in the final answer, so do not worry about rounding in the middle of a problem. For the final answer, I would determine the number of sig figs based on the number that has the least number sig figs in the original problem.
Sig figs are mostly used in the final answer rather than throughout all of the steps in the equations. Though, it's a good idea to keep 3 or 4 digits after the decimal just so there's greater accuracy in the final answer when rounded.
I would definitely use 6.626*10^-34 when doing calculations since it is more precise. If you're concerned about sig figs, just remember that they don't matter so much during the process as they do in your final answer. Use the least number of sig figs in the given values to determine how many you include in your final answer.