Hi, and welcome to the forum.
I can't answer all of your questions here and now, but there are others who might have some input to offer in regards to .243 bullet choices for deer hunting, etc.
I can say the Accustock has an aluminum rail that runs beneath the action and down the majority of the length of the forearm. If you remove the screws under the action (all but the rear-most screw which attaches the rear of the trigger guard to the stock), and inspect the interior of the stock, you will immediately see the aluminum rail. Also, you can normally see a portion of the rail by looking down into the forearm of the stock, along the barrel, into the barrel channel...
As for the name of the barrel... Call it what you want... "Bull Barrel" is normally a barrel with no taper. It will be a full 1 inch diameter or more all the way to the muzzle. Rare except with target rifles. "Varmint" is usually tapered somewhat, maybe down to about 3/4 inch diameter at the muzzle. "Heavy Barrel" is maybe something heavier than a "Sporter" barrel, which is quite light weight, tapered rather aggressively from about 3 inches in front of the action. "Heavy" is maybe synonymous with "Varmint".
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