What happens when using an external hard drive as the primary library?

There is no difference in use with the external drive.

• Has anyone regretted doing it and wished they had just chosen thumbnails and kept the library on their Mac?

No. If you don't have space, you don't have space.

• Did you delete the library from your Mac? Did you copy it to a 2nd hard drive as a backup?

Yes. Why take up space. Beside, you are likely backing up to another hard drive using Time Machine or equivalent, right?

• Does iCloud work the same? i.e. will my photos automatically in real time download and upload to iCloud?

Yes. As long as it is your system library and iCloud is on.

• All my people thumbnails are currently greyed out. Will they eventually all come back?

Have not experienced this. Are you certain your transferred the entire library file?

• Any suggestions using Photos this way?

Nothing should be different.

That's why you have the Time Machine backup; perhaps others as well.

A good rule of thumb is to keep 3 copies of your most important data, made 2 different ways, with 1 copy kept offsite. In my family I have my photo library on my Mac, synced to iCloud, and backed up onto my Time Machine Drive. We also burn to m-disc DVDs each year and provide copies to family. Our family photo history goes back to the 19th century so we also maintain a healthy number of original prints too. Backing up and planning for catastrophe is worth the time/investment.

Yes. So long as you do not exclude the drive from your Time Machine settings.