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It is possible, albeit a lot slower, to break up a rock using water. You would do this by freezing and thawing the water. You could create some initial holes or cracks in the rock, then pour water into the cracks or holes and allow them to freeze (so it's best to do this in winter or in colder climates). Since water expands when it freezes, this puts pressure on the inside of the rock and causes it to crack. You could continue to pour more water in and let it freeze to continue to break up the rock.

You should generally drill into the mortar joints when installing shutters on brick. Mortar is softer, which makes drilling easier and puts less strain on your tools. It also lowers the risk of cracking a brick—something that’s a lot harder to fix. Mortar holds fasteners well enough for standard shutters, and if you ever need to patch the holes later, it’s a much simpler job than dealing with damaged brick. Just keep in mind that if your mortar joints are too thin or the hardware calls for brick anchoring, you'll need to check the manufacturer’s recommendations and adjust accordingly.

Rock salt and ice melts contain sodium chloride, aka salt, and are corrosive to metal and concrete. If used frequently over time, it can cause corrosion, discoloration, chipping, and cracking to patios, walkways, and driveways. You can try a rock salt alternative or hire a professional snow removal company instead. 

Minor hairline cracks in mortar are normal over time. This is a natural occurrence as bricks settle. You should worry about cracks in brick if you see vertical cracks that widen as they move up, stair-step cracks, L-shaped cracks, or deep horizontal cracks. These are all more serious signs of foundation damage.