Can Veeam back up directly to a NAS?

Yes, it can

Yes you have a lot of options by selecting Repo’s Backup Repositories - Veeam Backup & Replication User Guide

But be aware of security/immutability on Repo’s and take care of the 3-2-1-1-0 rules as a guide.

Yes it does as I use Synology NAS devices and back up to them without issue.  Just depends on how you connect them as a repo as different protocols are better than others.