Do I need Adobe Acrobat Reader DC to replace Adobe Flash Player

Those are completely different software products. While Adobe reader is still available, Flash will be gone in approximately 2 weeks. Adobe Reader would be used to read PDF files, which can also be accomplished with Apple’s Preview app.

H.264 automatically replaces Flash player, and it is built into everything worth using.

You're good to go. Don't download anything.

Yes, Adobe Reader is a freebie, although I’ve never had the need for it.

https://acrobat.adobe.com/us/en/acrobat/pdf-reader.html

For reading and printing most .pdf files, the free version of Preview, already installed on your Mac, works just fine.