So I've shared the 3 core books with my D&D group and they can create their characters using all of those details.

Can they make other characters on their accounts using the same content I've shared or is it limited to a single character made and linked within my campaign?

Test it out!  That's the best way to see if it works that way.  I think you can, though.

It seems like you can't. I'm unable to verify directly as I have the books purchased but people im in a campaign with who have created a Cleric had full access to all Domains but creating a character outside the campaign only lets them choose Life. 

I hope this is a bug rather than forcing people to buy all the content if they want to have more than one character to create.

Excellent, thanks Stormknight and subsistcyber for getting in touch.

So it looks like you can make another character in the same campaign. It's a shame you can't just make one outwith any campaign and add them in later but for now, it lets them play around with the builder.

Do you know if there is a character number limit for a player and/or campaign?

12 players (or PCs) per campaign and 6 PCs (total) for a non-subbed Player. If the Player has the Hero tier sub they can make all 12 PCs if they wanted.

they can within the campaign, but they cannot outside of the campaign.  (Question 17 of the FAQ).  

Essentially you share the "compendium" content and they can view that as it isn't character specific, but as far as editing/creating characters and adding the toolset features (races/classes/items/spells) that come with the purchased content, that character must be in the campaign.

You can't have friend 1 in campaign A whom you share content with, create Campaign B himself and create another character in that 2nd campaign using the content you shared in Campaign A, unless he or someone else in Campaign B have unlocked that content.