I have not made up all my missed prayers.(Though I am trying.) Is it permissible to make Tahajid in this state?
It is permissible, in fact, encouraged to perform Tahajjub Salaat.
However, you should also endervour to fulfil your Qadhaa (missed Salaats)
from the time of attaining maturity. You are fortunate as you are still in
your 20s. You should embrace the opportunity to set your record straight
with Allah whilst you are still young.
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai