Can I delete my local photo library now that all my photos are on iCloud?
Yes - if you trust Apple to never lose the photos, you can delete all your local copies.

Pay attention to which devices have full resolution images and which have "optimized" settings.

Also, I've been doing this for iTunes Match for some time. I have only lost a few dozen songs in two years of trusting the cloud. For that reason, I now set alarms every 6 months to download a local copy of all the songs from iCloud and back that up to an external HD. I'll be doing the same with my iCloud photo library to be sure I never lose all the photos.

I would add, that if the thought of losing a dozen photos or having to wait several weeks if your account should get messed up for engineering to work out the problem isn't your cup of tea, you might keep your originals on hard drives and in filesystems you know you have the tools to work with directly.