Learn Turkish: Bizim soy ağacımız ne kadar eski acaba? - I wonder how old our family tree is?

The particle acaba (I wonder) is very flexible in Turkish. Placing it at the end softens the question and makes it sound like you are pondering out loud, much like saying 'How old is our family tree, I wonder?' in English. You could also put it at the beginning (Acaba bizim soy ağacımız ne kadar eski?) with the same meaning.

How exactly does the word ağacımız break down?

It comes from the noun compound soy ağacı (family tree, literally 'lineage tree'). When we add the first-person plural possessive suffix -mız (our), the original possessive -ı is replaced, and the hard ç in ağaç softens to c because a vowel follows it. So, ağaç + -ı + -mız becomes ağacımız.

To ask 'how old', why use ne kadar eski instead of kaç yaşında?

You use kaç yaşında (at what age) when asking about the specific age in years of a person, animal, or sometimes a building. For an abstract concept, an object, or to ask how far back into the past something goes (like a family tree), we use ne kadar eski (literally 'how much old' or 'how ancient').

Why isn't there a 'to be' suffix like -dir at the end of eski to mean 'is'?