1- Yes
2- In my opinion yes, I heal on a controller and its a pretty smooth experience
3- Each class has other classes which they can gain skills from. Its not a big deal to wait till your are over 40 or 50 to get them, but it makes for a much much easier experience to get them early. The most important one for you as a healer is swiftcast, which is crossclassed from THM at lvl24 or 26, I forgot .
As a healer you will gain skills from arcanist and thm. Prioritize getting swiftcast if you can.