1) There is supposed to be a lot of aggregate so close to your foundation. It was put there on purpose and under your foundation to stabilize the slab that rests upon the gravel that rests upon the ground. If you are going to contact your builder or the local building inspector you might ask them if they installed a water barrier (taped sheet plastic) under your slab foundation (maybe even foam insulation, considered a best practice) designed to keep moisture (and radon gas) from intruding into your home through hairline cracks that could develop in the cement slab. The plastic sheeting water barrier is important under slabs to prevent mold in carpeting, etc., because concrete like brick can absorb and hold a lot of water that needs to go somewhere to vent itself off (either the ground below, out the sides, or indoors). Whether there is a lot of gravel elsewhere on the lot would require digging and checking, and even then some of it may be where stuff was piled during construction for use in various places.
2) USA Home Inspectors would highly question the appropriateness of planting plants so close to the foundation as the root system can deteriorate cement over time, as well as hold moisture near cement and the side of your home, plus when you water it, you keep that area wetter than elsewhere on your lot. It can cause rots on exterior walls, damage paint, and damage the concrete over time.
3) Some of your responses have already suggested that your problem may be a drainage issue and not at all a water table issue. Since clay slows the drainage of water in the ground (and it is used at the base of man-made ponds for the same reason), it should be puddling somewhere, though you would certainly hope that it is not right up next to the house.
4) Drainage seems to be the key and that may require someone familiar with your lot location, the various slopes around your yard, as well as clay issues above the aggravate under and adjacent to your foundation. A knowledgeable neighbor (or a soils expert or building inspector) may suggest adding a lot of pebble gravel and sand around the house next to the exterior walls to improve drainage, depending upon how deep the clay is, as well as digging swales that direct rain water and snow melt to go somewhere else than toward your foundation. Planting a large tree 20 feet minimum from the side of your house (to prevent root damage to any in ground piping and your foundation) will one day lessen the amount of rain that hits the side of your house.
4.A.) In Wisconsin, where I live, I installed "ground gutters" all around my house, partially to thwart snow melt on the north side of my house and wind-driven rain on the west and south sides of my house (e.g., to keep water out of my basement and to stop the white fuzzy-looking growth, called efflorescence, on my inside basement walls, which was salts leaching out of the cement block because of moisture moving through the walls (and evaporating once inside my basement...but that adds moisture to the basement that can easily grow mold). The ground gutters ceased basement flooding, cement cracks, and the efflorescence (the fuzzy growth that people sometimes confuse with mold). These are sheets of plastic (I overlapped them by 9 inches minimum) buried under the dirt about 1 foot, and sloped away from the foundation. They carry and direct the rain that drops down from my exterior walls away from the house, and when it reaches about 12 inches depth in the soil. It is a cheap improvement, costing me only about $20 for plastic and my time. It took me 6 hours to dig out, install, and recover about 140 feet of ground gutters. BTW, in WI these are legal, and are recommended in certain home jurisdictions for problematic water near foundations/basements. Now depending upon how deep your frost level is during winter, what some people do is lay 2" - 4" closed cell foam boards at an angle sloped away from the house. The reason why they do this is that these foam boards help insulate the ground from freezing; and as you may know (or guess) frozen ground "heaves"--that is it moves up and down (as it freezes and thaws, which can happen often during each winter) depending upon how deep the frost level is. So if you have a side of your house that gets much colder in winter than other sides of your house, you might consider planting closed-cell foam boards (covered with plastic) because frozen ground is going to put a tremendous push (thousands of) pounds-per-square-inch onto your slab and may eventually crack it (and of course in the worst places...under and exterior wall). I recommend you contact a highly experienced home builder (not your home's builder) to advise you on these ideas. Four inch closed cell foam boards is much more costly than plastic (6 mil), but if you can get away with laying it in the ground around only part of your foundation that will decrease the overall cost plenty. BTW, contrary to prevailing opinion in WI, during extremely cold winters (e.g., cold winters with no snow on the ground, which insulates ground from cold temps), the ground can freeze much deeper than the official reported "frost level" (our area about 36"). Frost heave pushes up porches, breaks up concrete slab (you should see my detached/unheated garage), sidewalks, breaks up driveways, and can lift and change the shape of decks. It is much cheaper to insulate (in the ground) adjacent to ground structures (sidewalks, driveways, foundation, etc.) than to pay the price to install a new slab, new driveway, new sidewalks, etc. Sorry to be so long with this info, but it is important info that many don't know about, and it may be valuable to consider when you think you will have to make an improvement to your lot.
5) Make sure (if you have roof gutters to catch rain water and direct it to the ground) that you have a gutter extension that goes out about 4 feet or more from your foundation. If the gutter extension at the bottom of the downspout only goes out 4 - 6 inches you may never correct this problem having clay puddling the water in your soil next to your house.