Yesterday at one o'clock I was having/had lunch. - Yes. -- No.
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Hi.., here is my opinion
1.Yesterday at 1 o'clock I was having/had lunch.Both are ok.
Past simple can also show the action was in progress > No.
2.use past continuous because it tells about the action began in the past and is still going on at the time of speaking. He was walking along the river when the boat passed.
3. Can use simple part or past continuous.
4