Is this parallel?

[Brinestone]

If there are no results, then further research or another date range is needed.

I'm looking at the independent clause ("then further research or another date range is needed").

Problem #1 is that this is in passive voice. However, for the sake of argument, let's say I want to leave it that way. The actor(s) of "is needed" have been clipped, which is fine in passive voice.

However, if I were to revise the sentence to make it active, it would look something like this:

If there are no results, then you will need to do further research or enter another date range.

There really isn't a way to add in an actor, make the verb active, and leave the sentence intact.

Which makes me suspect that there's something wrong with the passive itself.

Hm. What do you think?

[Jonathon]

It's grammatically parallel, and I'm not even sure it's passive. It may simply be a participial adjective; you could replace it with "necessary" without changing the meaning.

However, it sounds a little weak to me because you're following a punctual verb with a durative one: "If x happens, then y is." States of being don't typically hinge upon events.

Your active rewrite solves this, and I think it sounds alright, too. But maybe you feel that a generic actor wouldn't be appropriate.

[pooka]

Avoiding "you" is a pedantic but nonetheless standard rule of professional writing.  The only thing I wondered about was the "is" in the end.  But I think it's okay.

[Brinestone]

Considering this is in an FAQ section, I think it's appropriate to use the second person. That's not a concern at all.

[pooka]

How about "if that doesn't work, you..."