What is the ruling regarding someone who pledged to pray Qiyam al-Layl and confirmed it with a thumbprint, then forgot his commitment for a period? How does he atone for the days he forgot, and is a single expiation sufficient, and what is the obligatory expiation?

Merely placing a fingerprint on a paper without uttering an oath or a vow to commit to night prayer does not obligate anything. An oath by Allah is only valid by His Name or His Attributes, and it is not established by writing. If you swore not to abandon night prayer, and then you forgot on some days, you do not break your oath by that, according to the preponderant opinion. However, if you offer expiation as a precaution, it is good.