They don't call them window shakers for nothing. Knowing what the rattle is (window or unit itself) is important to know. It could be the front cover unit or, most likely the filter itself. Take it out the next time the rattle starts and see if the rattle goes away. Over time, window units begin to lose their "tightness" and you'll notice various vibrations. One of the culprits might be the fan blades. No matter how careful you are with the filter, the inside blade can pick up dust. The outside blade most certainly picks up dust as well as getting corrosion on it. These things throw the fan out of balance just enough cause annoying vibrations. You can put foam strips wherever the unit actually touches the window sill, sides and upper portion which the window lowers down on, to help damper the unit from the window frame, if that is where the rattle might be. Just an fyi...turning the unit on and then off and then back on can cause problems. From your description, it appears the noise starts when the compressor starts which in itself will cause vibrations. The mounts holding the compressor in may need to be snugged down. The compressor mounts are rubber and of course rubber hardens and is not as resilient as when new. But when you turn the unit on and then off and then back on, the noise may stop because the compressor is not running. There is a safety device which prevents it from starting right back up because that could damage the compressor. The overload protector trips in the compressor circuit (for 3-5 minutes) because the refrigerant pressures need to equalize and then trips back to let the compressor come back on. They are not designed for repetitive functioning and you'll wear them out faster. Some are external and can be replaced but, some newer units are built into the compressor and cannot be replaced. So, don't cycle the unit off and on to get rid of the noise. The next time it makes the noise and you determine it's not the filter or the front cover rattling, try grabbing opposite corners at the front of the unit and putting pressure first one way and then another. If this stops the noise, you'll know which side you'll need to shim. I hope this helps!!

Several thoughts. Usually the only storm windows I encounter that rattle are aluminum storm/screen combinations mostly from the 1950s and 60s. By then the weatherstrip (if any) is pretty worn and it's easy for them to rattle. If that's the case for you then it's time to consider replacements. If they're newer storms and they rattle, perhaps you could buy replacement weatherstrip and insert it into the storms in place of the old weatherstrip, presumably when it warmer out this spring. It's a slow putzy job but would hopefully solve the problem. If replacement is not an option, then the foam rope you mentioned is certainly worth considering. I consider this a "band-aid" approach that addresses the immediate problem but doesn't completely solve it, but it is a cheap short term solution. Newer well-made storms shouldn't rattle at all; it's unfortunate that you're stuck with some that do.

If the thru the wall unit is rated for 20A, then yes, use the existing 12/2 wire for 240V. Simply take out the 1 pole breaker and replace it with a 2 Pole breaker, making sure the new double breaker is attached to different legs in the panel. If you don't know how to do this, check a wiring book. Then attach the black wire to one breaker of the pair, and the white wire to the other breaker. Place some black electrical tape on the white wire at the panel and the new unit. If the new unit is 15A, then use a 2 Pole 15A breaker. If the new unit is rated at 25A or more, you will need to rewire as well as bigger breakers, assuming you now have 12/2.

If the window rattles when you walk across the room, the problem would likely be the responsibility of the structural engineer, the architect and lastly, your builder, as it may be a structural issue. Walls systems should not vibrate from floor joist movement when moderate weight is applied. The leak should not be related to the rattling glass muntins. If you are able, place a ladder on the exterior wall and check the seal around the window frame at the top. Also, check the seal between the window frame or sash and the glass to ensure the water has not penetrated where the glass meets the window frame/sash. The top of the window should have flashing and caulk or silicone. The area where the glass meets the window frame/sash should have solid contact with some type of waterproof membrane (i.e. butyl, caulk, silicone). Lastly, if it is a window fault, the problem is the responsibility of your builder if they selected the window manufacturer, or if they were the party that provided payments to the window supplier. The contractor would be the party to contact the window supplier and would likely receive a quicker response, as the supplier would want to ensure a continued relationship with their client, the builder. Be sure you do not delay in resolving this issue, as most builders do not warranty their products beyond one year.