Can liver regenerate itself at any age if a part of it has to be removed? or it only regenerate itself at relatively young age?

Depends.: The liver can regenerate at any age, depending on how much liver is removed. Also, there are appears to a decrease in the ability to do so as we age. It also depends on overall health. Here is a general discussion: https://en.wikipedia.org/wiki/Liver_regeneration Here is a complex discussion: https://www.hindawi.com/journals/cggr/2011/526379/