The speed of light is 299,792,458 m/s (by definition)
We normally use 300,000 km/s for astronomical calculations.
The 'year' used is the Gregorian year, the year on which the western world's calendar is based (365 days, one day added every leap year -- a year divisible by 4 except century years not divisible by 400).
A gregorian year is 365.2425 days of 86,400 seconds = 31,556,952 seconds.
A light year (distance travelled by light in one year) is 9,460,536,000,000,000 m (I have rounded the figure a bit) or
9,460,536,000,000 km (5,912,834,600,000 mi).
It is 63,239.8 AU (astronomical units, the average distance between Earth and Sun).
Eta Carina WAS 7,500 light-years from us when the light left. So we are seeing it as it was 7,500 years ago.
The further away we look, the further back we see. As we look further back in time, the universe appears different (younger). This is one of the hints that make astronomers think that the universe had a beginning, because we cannot see past a certain distance (14 billion light-years).
The universe could be much bigger than that (or not), but the light from anything further out would not have had time to reach us if the universe did begin 14 billion years ago.