1) You are having trouble signalling because you think that you steer with the handlebars. I say this because I just recently taught my daughter how to ride and she did the same thing.
A wheel in motion WANTS to stay upright and straight. You don't HOLD it straight.
Try this: Find a hula-hoop. Roll it. Notice it stays very straight and rolls upright until it slows down, then the effect wears off and it starts to dip to one side. Nobody is balancing that hoop; due to its motion it wants to stay upright. Your bike is two of those hoops bound together.
The handlebars are to steady you, not for you to steady them. You don't steer with your handlebars, you steer with your body, even if you don't realize it.
Try this somewhere safe: Start riding in a straight line. Now, sit up more so your weight is mostly on your saddle. Un-grip your handlebars so your hands are on top of them but not circling them. Try to keep your touch as light as you can, like a feather. You'll find that, with a super light touch, you still feel secure and steady (you might have residual fear). Because your touch is so light, it is pretty much nothing to take one hand slightly off. Once you can do that you can signal and still feel secure. Nothing about your riding has changed other than your anxiety.