My 2017 federal tax return is under review by the IRS. Should I wait to hear from the IRS before I file an amended return if I know where the mistake occurred?

Yes, wait to Amend, however, if they happen to be still reviewing and April 17, 2018, is getting close I would go ahead and Amend and pay any additional tax to avoid and additional interest and penalty.

However, if they are reviewing right now, hopefully, they will be contacting you shortly. 

I just had my return referred to another department where I was told it could take up to 8 weeks to review putting the date around 5/30/2018. I do not owe taxes. The review is based on the solar tax credit refund. Should I still wait to hear back from the IRS before amending the return then?

No, then I would Amend now as if you owe money there would be interest and possible penalty.  See this link for amending.  <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/replies/3288565">https://ttlc.intuit.com/replies/3288565</a>

Even if I was going to get a tax refund back before I even used the solar tax credit?

If you want to be safe I would, what if they disallow the credit?  This is your call, as I do not know how much money we are talking about.  If you are 100% sure about the credit, then just file the amended return (with no payment)

I will get a refund for the solar tax credit.  That is not in doubt.  The mistake was based on the wrong amount entered.  The amount entered should have been $11,000 whereas I entered $13,500 based on wrong information.  I just did not want to file an amended return if it was going to delay the process more.

I understand the Amended return should be sent to the department reviewing it and then it would be incorporated into the original as part of the review.  The key word here is "should" and I would Amend myself if it was my return.