Will screen sharing work across different ISPs and over the Internet?
This question is quite broad, and there is no succinct answer. Many ISPs have filters on their networks and do not pass all IP protocols transparently.  I have experimented with Chrome Remote Desktop, however, and it seems to be work very well. I can access to my home iMac (on Verizon FiOS) through my school's firewall without a problem, and with my iOS devices, too! You might want to experiment to make sure it does what you need.