Response: To say the Belleville Senators are an American team is like saying that the Ottawa Senators or the Toronto Maple Leafs are an American team. Yes, they will be playing in the American Hockey League, that is headquartered in Springfield, Massachusetts. No, that does not mean that they are an American team. They will be playing in a Canadian city, and they are owned by a Canadian group.
Furthermore, there will be four Canadian teams in the AHL by the start of the 2017-18 season: Belleville (Ottawa Senators), Toronto (Toronto Maple Leafs), Manitoba (Winnipeg Jets), and Laval (Montréal Canadiens). Also, just because the NHL is based in New York, doesn't make it an American league. Plus, there were American-based teams in the Ontario Hockey League, but they were still American!
Answer: To answer the first part of the question it is important to note that Eugene Melnyk and the ownership group didn't just decide on a whim to pick Belleville as the site for their AHL team. Several months and a lot of analysis and planning went into the decision to pick Belleville. While it would be ideal if they could move even closer to Ottawa into more traditional "Sens territory", Belleville is the ideal destination for various reasons (as explained in my previous article) with the primary reason being market size/population. Additionally, there are still a lot of Ottawa Senators fans in the Quinte area.
For the second part of this question, it's important to note that there is no "correct" answer. In a way, yes, if you are a Maple Leafs fan, by supporting the Sens you would be cheering for your rival's farm team. However, the actual competition between the Senators and say the Marlies, is all about the development of all the players on the ice. So a good game of hockey between the Marlies and Senators at Yardmen Arena, would be beneficial to the development of the players on both teams.
In short, yes you can be a Senators fan, even if you are a Leafs fan.
A: The Bulls did not simply leave Belleville because they were not supported, and to say that they weren't supported isn't entirely fair or accurate. Yes, there was a decline in attendance which may suggest lessening support, however, there were a plethora of reasons that led to that decline in attendance. With a new team that will be playing in a newly (and much needed) renovated arena, there are plenty of reasons to expect a very well supported franchise. For one, more seats means that overall/average ticket prices do not need to be as high, because there will be more tickets sold. This was a problem the Bulls had, with nearly 2000 fewer seats than the average OHL arena; they had to charge more to make up for the fewer number of tickets purchased.
With the Senators, ownership, local government, and fans seem to be on the same page - and that is a very promising start to this new partnership.
R: Just because a player has made it to the AHL, does not mean the effort will decline. If anything, the players will be working that much harder to make the final leap to the NHL. You can think of the AHL as a Canadian Hockey League for older players, or the last hill to climb before reaching the summit. Many of the players drafted to the NHL will spend at least some time with their club's farm team before they put on an NHL jersey. The effort will be just as intense, if not more intense, for these players looking for their big break, or who are looking to return to the big league.