Geralt is around 90 - 100 years old.
Yennefer is around 110, while Triss is way younger (around 50).
Ciri is around 25 in most of TW3 (except the beginning of course where she should be around 12).
Vesemir is around 200. The "probably older than Kear Morhen" is not meant literally, I think that's a euphemism.
The reason why Witchers live so long is their mutations. They make them immune against most poisons and illnesses, which means they can only die of old age. Add their improved metabolism, high cell reproduction (better healing abilities) and other mutations and they can grow very old.
I mean if you think about it it makes sense. After all all that lets us humans age are the limits of our ability of cell and DNS reproduction. Would our cells have higher reproductive capabilities and would our body contain more telomerase which could produce telomers, the endings of our DNS that do not contain any information but prevent that our DNS is "cut short" while copying it (because that is unfortunately happening), we would live longer. In fact, I think scientists just recently discovered a gene that could increase out cell reproduction abilities, so a "jump" in age-limitations might not be so far away in todays world.
Sorceresses and Mages grow old due to their magic, and their appearance is most of the time formed by magic. They change themselves to look attractive. Not a n illusion mind you, more like a transformation done by magic over the years (on purpose by the mages themselves). I think Sorcerers and Sorceresses can become around 300 - 400 years old according to the books, while Witchers COULD live a little bit less long, though most die between 20 and 150 (no specifics were ever named, those latter numbers are only estimated) due to the nature of their work.
As for Ciri, well, she isn't old yet, but considering she had magic abilities AND has elven blood (elves grow hundreds of years old) in her veins it probably means she could get very old as well.
