I haven’t played DIII for years so pls bear with my seemingly dumb question.
Are paragon points shared between characters? I had a previous character with a paragon level of 69 (I believe). I deleted that character, started a new character and immediately, I have some 18 paragons to spend for each of the 4 catagories.
Does this mean if I start ANOTHER new character, I would again have 18 paragon points to spend in each catagory?
Yes, paragon levels are gamemode wide. All characters in the same mode share paragon levels.
Non-season paragon points are shared by all characters on the account per mode, i.e. all hardcore chars share hardcore paragon levels, softcore chars share softcore paragon. Seasonal characters also share paragon per mode (softcore/hardcore/SSF softcore/hardcore), but they only have the paragon levels earned during the current/active season. So your seasonal characters won’t have the same paragon levels as your non-seasonal characters. Seasonal paragon experience (not levels) transfers to non-season at the end of each season. I hope this helps. 
(Kirottu types faster than I do.)
Thank you very much for the help, guys.