To fill in the blanks with suitable verbs, let's think about the context of each sentence and what action would make sense:
Tom was playing computer games all day yesterday.
'Playing' is a suitable verb here because computer games are typically played.
It was raining when I came back.
'Raining' is often used to describe weather conditions happening outside.
He was washing up while she was sweeping the floor.
'Sweeping' is an appropriate action related to cleaning the floor.
The pupils weren't listening while the teacher was talking.
'Listening' fits well here because it relates to paying attention to someone speaking.
The baby was crying all night.
'Crying' is something babies commonly do, especially if they're uncomfortable.
While one tailor was measuring, another one was cutting the cloth.
'Cutting' is often what tailors do with cloth to prepare it for sewing.
The maid was dusting when the phone rang.
'Dusting' is a common household chore that involves cleaning surfaces.
The boy was still sleeping when the alarm clock went off.
'Sleeping' makes sense since alarms are set to wake someone up.
She was looking at the mirror when it broke.
'Looking at' is a simple action involving mirrors.
The southern wind was blowing strongly the whole evening.
* 'Blowing' describes what wind does, especially when it's strong.