In Mahabharata, how did Bheeshma know that Karna was Kunti's son. Who revealed it to Bheeshma?

 Bhīṣma knew that Karṇa was Kuntī’s son through Devarṣi Nārada, Kṛṣṇa Dvaipāyana Vyāsa, and Bhagavān Kṛṣṇa (Keśava).

On hearing that Bhishma had been brought down, Radheya, bull among men, swiftly came to him, partly because he was terrified. He saw the great-souled one, lying down on his bed of arrows, like the lord, the god Kartikeya, lying down after his birth. The brave one’s eyes were closed. His voice choked with tears, Vrisha (Karna) worshipped the feet of the immensely radiant one who had fallen down. ‘O best of the Kurus! I am Radheya. I have been in your sight, but you have always regarded ‎me with hate.’ He spoke these words. On hearing these words, the aged Kuru used his strength to slowly open his closed eyes and glanced at him. He spoke these affectionate words. He asked the guards to leave and once they were alone, glanced at him with benevolence.

‘“Gangeya embraced him with one arm, like a father towards a son. ‘Come. Come. You have always been my adversary and have always sought to rival me. If you had not come before me, there is no doubt that it would not have been good for you. You are a Kounteya(son of Kunti). You are not Radheya. I have known this from Narada and from Krishna Dvaipayana and Keshava.

• ‎CHAPTER 977(117) Bhishma Vadha Parva, Mahabharata

What was the approximate age of Bhishma when he died?

 Bheeshma (3394–3138 BCE) died at age of 256 years in war. He was contemporary to Magadha king Satyadhruti (3394–3351 BCE), who was great-great grandfather of Jarasandha (3222 - 3180 BCE).

When Bheeshma was young, ready to get married and become king, his father Santanu wanted to marry Satyavati, a fisherwoman. Bheeshma gave up his marriage to get his father get married again. Satyavati already had a pre-marital son (Vyasa) with sage Parasara.

Santanu had 2 sons Chitrangada and Vichitraveerya with satyavati. These 2 sons were step-brothers of bheeshma but in age they were 1 generation younger (almost his sons age). Chitrangada died in a dual with a gandharva with same name. Vichitraveerya was a kid at that time and upon request of satyavati, bheeshma ruled on his behalf until he becomes an adult. Which means vichitraveerya is much much younger (almost grandson age of bheeshma, though technically a step-brother).

Bheeshma went to a swayamvar and brought 3 sisters (amba, ambika, ambalika) for Vichitraveerya, out of which amba did not stay.

After few years, Vichitraveerya died of tuberculosis without having kids. Satyavati called upon her first biological son Vyasa to impregnate her daughter-in-laws.

Dhritarashtra, Paandu were born to them (along with Vidura to a maid). these 3 were almost 3 generations younger to bheeshma. Their sons Kauravas and Pandavas were technically grand-children to bheeshma, but were 4–5 generations younger.

Dronacharya was 150+ at time of kurukshetra war.

Karna 107

Yudhishtir 91 (kunti had her 2nd biological son 16 years later)

Bheema, Duryodhan 90

Arjun, Krishna 89

When pandavas were leaving for forest, Krishna meets them, takes blessing from yudhishtir and bheema (they’re elder), hugs Arjuna (same age), blesses Nakul,Sahadev (younger than him).

Draupadi must be 60+ at that time as she was born only after Drupada lost war to arjuna (when dronacharya asked to bring drupada as guru dakshina), and he performed yagna to get a son who can kill Drona and daughter who can marry Arjuna.