1. Yes, but finding them is tricky.
2. Radio telescopes work the same way as optical ones, it's just that the wavelength is a lot longer (about a million times). Of course you cannot look through an eyepiece at the image, but need a detector in the focal plane to record it.
3. All else being equal, limiting magnitude goes like log(aperture sqared)/log(2.5), or about 0.5 magnitude increase with every 25% increase in aperture. Trouble with binoculars is that all else is not equal, because the magnification is fixed. I can easily pick up mag 9-10
galaxies with my 20x90.
The reason to get binos is the wide true field of view. just on aperture, a 6" or 8" scope will show you a lot more, and when you consider higher magnifications attainable with the scope, more still.