A person's 'lap' is the flat area between the waist and knees of a seated person . We only have one per person, so it can only be 'on my lap'.
I had a dog but now it's dead" is correct
"I had to travel by train on the 12h and I read all the way."
We say, 'counterfeit money', and colloquially, 'fake money', and, 'that note is a fake'
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