Let's get the grammar out of the way. And I'm going to simplify your example and stick with love and drop like. The sentence in your title
[1a] *Do you love a person also have the wrong?
is both ungrammatical and unidiomatic, and in ways that make it difficult to guess what you mean. If you mean that the subject (you) both loves and is in error, you could say
[1b] Can you love a person and also be wrong?
But it's not clear whether you mean that it's possible to think you're in love and be mistaken or whether you mean that you're actually in love but that love is morally suspect.
The sentence in the body of your post is also ungrammatical:
[2a] *Is there anything wrong to love a person?
This phrasing requires a gerund in a prepositional phrase, not an infinitive as a complement:
[2b] Is there anything wrong in loving a person?
An alternative that keeps the infinitive:
[2c] Is it wrong to love a person?
The questions in 1b, 2b, and 2c seem to invite such trivial answers. Part of that arises from the use of the simple present tense (is), which is often used to describe a general rule or ongoing situation. I suspect that you mean something different, something that pertains to a particular situation, perhaps something like "Can you love a person without consideration for right and wrong?" If that's true, then you might find the following sentence useful:
[3a] The heart wants what it wants.
The heart here is considered the seat of emotions, particularly the romantic, and the sense here is that the heart wants what it wants without consideration of the consequences, i.e., people love without thinking about right or wrong, good consequences or bad.
From your comments, my initial guess isn't quite right. The specific situation you have in mind is unrequited or unreturned love, and what is wrong is that the person who loves is disappointed. In this case, I recommend
[3b] Can you love the wrong person?
Here the word wrong doesn't speak to a moral judgment but about the appropriateness of the person loved. Here we have the auxiliary verb can, indicating possibility. 3b asks rhetorically, "Is this situation possible?" Notice that the subject you is the second person pronoun, which ordinarily means the person to whom you're speaking, as in "Can you pass me the salt?" In 3b, it means any person, the equivalent of
[3c] Can one love the wrong person?
This is called the second person indeterminate. If, as you indicate, the disappointed lover is talking to himself, he or she might use the first person I:
[3d] Do I love the wrong person?