I remember a number of weird noises before I knew how to put the fairing back on properly.
One of them was a buttock clenching "I'm riding on wet tar" sort of noise - which came from the radiator grill.
I don't remember much about fitting the ST1100 fairing - its been nearly 20 years since I took one off and reinstalled it. But those push button clips must got through two holes before the button is pushed in. It is so easy to get it throught the first hole, and push away the plastic containing the second hole. So when the button is pushed in, nothing is fastened together. Make sure that the button is pulled out and check that the two holes into which it fits are both lined up properly - push a cross head screwdriver through the holes to manoeuvre them into alignment.
Then push the fastener in. Then push the button in to expand the fastener to secure both bits of fairing together.
I think that the fairing pieces have little tabs on them - one bit has to fit behind another bit. Sometimes there are two tabs one on one part of the fairing, one on the other part. When fitted together, the two tabs are next to each other - Each tab hidden behind the mating fairing - so the only way that you can do that it to offer them up to each other before anything is held in place. This is a common mistake made when taking the bike to the dealers. It can only be rectified by undoing everything and putting it together properly.
I can see the button at the bottom left of your photo- it does not look like it is holding the red inner fairing in the correct place - the edge is sticking out a bit in relation to the lower outer fairing - the red part on the bottom left corner of the photo.
The shoulder bolts. LIke the one holding the grey plastic - again in the bottom left corner. Hex socket.
These are not all the same. They are designed so that they do not clamp the plastic. When you tighten them, the base of the shoulder is tightening against the metal that contains the female thread. The broad flange of the head of the bolt does not press tightly against the plastic. It fits snug but not tight. That shoulder is fractionally longer than the thickness of the plastic that it supports. So the plastic is never put under any strain. Unless you have used a bolt that is supposed to go somewhere else in which case either the fairing will rattle aorund ont he shoulder, or the plastic will be clamped tight.
Sometimes - over the years - the cosy fit of the fairing pieces has become a little slack. This was the case the grey pieces of mine under the windscreen. There was a gap. One piece of plastic didn't fit snugly against the other. Maybe it has deformed slightly in the heat. I don't know. But the screen used to whistle annoyingly in the airflow. All it took was a a strip of ductape wrapped round the edge of one of the pieces for an airtight seal to be obtained.
You don't have this, but when you do - the pieces inside the housing with the timing belt at the front of the engine - well my overactive imaginationw as convinced that somethign in there was broken off, the timing belt would get out of synch and at any time I could be thrown over the handlebars. But it only happened at 2000-3000 rpm.
It turned out to be a cracked exaust shield - one bolt on the exhaust header was holding a circular piece of the shield. The rest of the shield with a hole in it was resonating.
But the one that took me the longest to solve - was a jingly high pitched rattle. It would never do it in the garage, only when I was out on a ride.
It turned out to be my house keys that I put in the lockable fairing pocket.