Length of longest arithmetic progression in an array
No, your approach is wrong. Consider the set of numbers $1, 3, 4, 6, 7, 8, 10$. The longest arithmetic progression(LAP) in it is $1, 4, 7, 10$, which is of even length. However, 4 and 7 are not adjacent items so your approach will not find that LAP.

Yes, your approach is correct, but to a different problem from the problem in the article you mentioned.