Today is the second day of Rosh Hashana, and it happens to be Friday. The holiday will end after Shabbat begins. Should we light candles today?
Yes, we always light Shabbat candles, and at the usual time (non-primary source). The only time a holiday affects candle-lighting is that on the second day of a two-day holiday, so long as the second day is not also Shabbat, you don't light the second-day candles until dark so as not to encroach the first day.
For Shabbat immediately after a holiday, or for the second day of a holiday, light the candles from a pre-existing flame (such as a pilot flame or long-burning candle lit before the holiday).
Yes, we should.
But I don't understand how can you ask this question on second day of Rosh Hashana. Using computer is forbidden on yom-tov.