After the ascension of the father-in-law to Paramapadam, during the first one-year period, can the wife or daughter-in-law take an oil bath? Is it appropriate to offer Sumangali women Thambulam on the evening of the father-in-law’s maasikam? Is this a practice?

It is not in practice for the wife of the deceased to take an oil bath; after the subhasveekaaram the daughter-in-law can take an oil bath.
I have heard Thambulam is offered only when a sraddha is performed for sumanagali sthree; have not heard Thambulam being offered for the ascension of a father-in-law.
It is considered auspicious if a very elderly person ascends to Paramapadam, Thambulam is offered then as it is considered auspicious.