Here is the sentence:
- Fifteen new people have been recruited and five resigned.
- Fifteen new people have been recruited and five have resigned.
According to me sentence number 2 is correct, here rule of parallelism is applied with and.
You're right — example 2 is correct. The first example is trying to have "been recruited" parallel with "resigned," and obviously they're not parallel. (The implication here is that those five people have "been resigned"—forced to resign, I suppose, or treated as having resigned without ever taking the action of resigning.) In the second example, it's placing "have" (been recruited) parallel with "have" (resigned), so the parallelism is sound.
Both of your sentences mix active voice with passive voice. In the first:
have been recruited = present perfect passive voice
resigned = simple past active voice
In the second:
have been recruited = present perfect passive
have resigned = present perfect active voice
Both sound idiomatic to my U.S. English ears, although the second is arguably more correct because of the parallelism between tenses. It's also arguably more clear since it prevents trying to read the ellipsis as "five (people have been) resigned." The word people is elided here no matter what.
However to address the question in your title, yes, it is common to mix active and passive voice. If you want to focus on a single subject who both did something and had something done to her, it's quite useful.
The nurse attended to five patients and was thrown up on once.
The teacher made a real difference in children's lives and was loved by many.