Does that plan require the cluster to spin up if you haven't had a visitor in a while? That's the reason I don't use Heroku for my personal site.
Regardless of where you host, if that's a problem for you, just set up a free account at Pingdom to hit it every 1 minute, and get uptime/response time monitoring as a bonus. Easy peasy.
Nope, EC2 is essentially a VPS host, unlike Heroku.
I bought a 3-year micro instance for my personal needs and it's been pretty good.