I paid my property tax late in 2016, with a check date in 2016, but it was not cashed until 2017. Can I count it as a deduction for 2016?

Yes.  If you're a cash-basis taxpayer (as most of us are), you take expenses in the year they were paid (check date).

Is this still true? My county website shows payment date as 1/29/2018. But, I wrote the check on 12/30/2017. Can I deduct it?

If you wrote the check in 2017, you can take it on your 2017 return.