Learn Russian: Это известный предок, жизнь которого мы обсуждаем. - This is a famous ancestor, whose life we are discussing.

While чей (whose) is used for asking questions, when you connect clauses to say 'the ancestor whose life', you must use the Genitive case of который. It essentially translates to 'of whom' or 'of which'.

In English we say 'whose life', but the Russian word order is жизнь которого. Is this order required?

Yes! When using the Genitive form of который to show possession, the 'owner' word comes after the object being owned. You are literally saying 'the life of whom'.

Since жизнь is a feminine noun, why does которого have a masculine ending?

Который always gets its gender and number from the noun it refers back to, not the object it owns. It points back to предок (ancestor), which is masculine, so it takes the masculine Genitive form которого.

What case is the word жизнь in here?

It is in the Accusative case because it is the direct object of the verb обсуждаем (we are discussing the life). Feminine nouns ending in a soft sign (-ь) do not change their spelling in the Accusative case.