Ok, Ciao, I used to live in Sicily, never hunted in Italy.
Question 1. Maybe.
Several things contribute to accuracy.
1. Condition and quality of the barrel
2. Harmonic function of the barrel and how that relates to the rifle action and stock. It is not very tight, and the barrel doesn't have the ability to flex the stock and or receiver can contribute negativly to accuracy.
3. Scope mount, and how well it controls the optic but does not impinge on the optic.
4. The optic itself and how well it is contained by the scope mount, and how tough it is in recoil.
5 The bullet and how it relates (shape, density, ogive, speed and bearing surface to the barrel).
So yes to answer your question, reloading gives you more control over my point 1 and 5. Saying that you must control everything else to increase accuracy.
But, your preferred bullet may or may not match well to your barrel.
To answer question 2. Yes you are correct. The higher quality the barrel and the better the tolerances are on the ammunition the higher odds that the ammunition will be accurate.
If you have an accuracy issue, you should always do 3 things.
1. tighten all bolts on the rifle to factory-recommended specs using a torque wrench.
2. verify your scope is working, swap it for another one and try that.
2. clean your barrel to zero, removing all copper and carbon (powder) fouling.
Then
1. Fire 10 rounds to foul the bore, do not clean it after this.
2. Try like you said 10 varieties of ammunition. Try to match the bullets to your desired characteristics. Choosing a common caliber like 308, 30-06, 6.5x55, 6.5 Creedmoor, 270, 300 Winchester, 7mm Remington Magnum , 7x64, or 8x57 will help. Common cartridges generally have more ammunition development than esoteric loadings. The 7mm Blaser is a perfect example of a cartridge that has one load.
3. Consider bedding an issue if you can't come up with an ammunition solution. For something that has a bedding block like a Blaser R8, Anschutz 1782, Sauer 404, Sauer 202 and other rifles you should not mess with the bedding block. For standard rifles Tikka T3, Winchester m70, remington 700, Sako 75, 85, AV, you need to bed the action to the stock. With somekind of compound like DevCon, or some other epoxy bed.
4. Shorter barrels always shoot better than long barrels. Consider having a very long barrel cut down to 22 inches for magnums or 18-20 inches for non-magnums. This is due the stiffness in the shorter barrels of the same dimensions. Don't believe me, try breaking a 8 inch pencil in half, and then try to break a 3 inch pencil in half.