why is "tôi là một người trung thực" incorrect? is it wrong to use the article 'một' in this context?
"Tôi là một người trung thực" is still correct. I added it.
Both of them are correct. We also use ''thật thà'' for this one (but I'm not sure if it's accepted or not).
Another question: why is "là" necessary here?
You need là if you're saying something is [a noun]. If you're saying something is [adjective] you don't need là.
Một is not even a choice to use in here
Why is "một" optional?
Yes, in the exercise, it is a "pick the right words to make the sentence" and "một" isn't even there to pick.