Judging by your question, you know that a year is proportional to the time it takes a planet to orbit the Sun, so when you go to figure out your age on the sun, it doesn't make any sense. The problem comes with the definition. However, if we say that a year is equal to the time it takes the Earth to complete a full orbit around the Sun, then we have no issues.

In general, humans tend to work pretty well with units between 1 to 100, so we invent units to keep numbers in this range. For example, you know when something is 100 feet, 100 yards, 100 miles, 100 lbs, etc. Once numbers get too big, we just make new units. (For computers, we have 500 MHz, 1.2 GHz, 200kB, 1MB, 500 GB, 1 TB; we usually don't let the number get bigger than 1000 before we change units, which is the whole magic of the metric system and just adding zeros.)

If I were on the sun, I wouldn't be calculating my age, because I'd be all burned up!

But if you're thinking about gravity, I don't think gravity affects our age. We weigh less on the moon, but I think we're the same age.

And if you're thinking about relativity and related things, I still think our age would be the same, because the sun and the earth and the rest of the solar system are all moving through space together.