DaVinci Resolve started as a dedicated color grading system, and its free version still beats almost every paid competitor on the market.
Yes. Blackmagic Design offers a genuinely free version of DaVinci Resolve. It is not a trial, it does not expire after 30 days, and it does not force a watermark onto your videos when you export them.
While the free version is generally watermark-free, you may occasionally see a grid-like watermark appear on your video viewer or final export.