In the US, you ride in the right lane as far right as you can unless you are "taking the lane," which is legal in some states under some conditions (e.g. no bike lane, debris on shoulder, not safe for car and bike to split a line - which in my opinion is never safe).
By signaling with your left hand, your hand is going to be more in the line of sight of drivers vs. your right hand which will be harder to see since you already are to the right of the road and even possibly in the shoulder area.
At the end of the day, you will probably never get a ticket for signaling with the wrong hand or not signaling at all, just do what you feel is safest for the situation.
In my opinion, a visible flashing rear light probably is going to catch the attention of a driver more than any hand signal unless flipping them the bird... just saying. I would not consider riding even on the shoulder of any road without effective visibility lighting (e.g. stuff from Bontrager has pretty good flash patterns to catch people's attention)
Regarding benefits of front vs. rear brake on bikes, yes it is true that the front brake is more effective for any 2 wheel vehicle like a bike or motorcycle. Furthermore, using both in unison is the most effective overall. With that said, most people on a bike are traveling at slower speeds than a motorcycle and so you can certainly stop a bike safely with just the rear brake. In fact, I usually drop most of my speed using both brakes and come to a final stop with just the rear because the rear brake at slow speed does not cause as much instability as the front (note the same can be said for a motorcycle in a parking lot where a lot of people use the rear brake only to control speed). Some of that is personal preference too.
Here is an example of a ride on a US road where I am taking the right most lane and if I was to signal my left hand would be most visible to a driver behind me: