Volume and clipping
If you have an installer, David, then it's probably level-matched na. It's one of those very important to-dos for an installer.
If David said that volume 47 is fine, then it probably is. If you want to really know where your maximum volume is, go back to him and ask that he test the clipping volume using an oscilloscope.
This is probably the best way since it's fool-proof.
Clipping is inevitable as everybody will clip at one point in their lives. So don't really freak out over it.. It isn't bad per se but its effects are. Duration and severity also plays a role.. for example, I sometimes turn the knob on my volume above clipping just to hear a damn-soft track but I don't mind it at all. As for the mentioned effects, it simply sends uhh... erratic signals for the amplifier.. which in turn generates excess heat.. and poof! that's how you blow amps and speakers
Some people say that 70% of the max volume would be your limit. However, this is not a standard rule as it's simply an approximation.. I believe this belief stemmed from the fact that most installers match their gains using the 70% volume rule. I've encountered head units that clip at 50% and I've seen head units not enter clipping just a notch below their maximum or even not at all! Take my Sonata for example, my maximum volume is 32 but my head unit starts giving out whacky waves (aka clipping) at 30.
Break-in
Mechanical break-in is the same as break-in... it's simply a more technical term. What break-in does is that it loosens up the speaker internals (voice coil, surrounds, etc.) hence "mechanical" so it's reaches its optimum sound. There are pro-break in camps and anti-break in believers. On what I believe it, I'm pro-break in.
Big Three Upgrade
I won't delve into the steps as you can simply Google it. But the Big Three upgrade simply improves the flow of electricity by upgrading three wire capacities of your system. Remember that your stock electrical system is designed to handle STOCK loads. Personally, my rule of thumb is that if I'm running 500W and above, I'd recommend this upgrade. In an analogy, think of it like getting water where water here is your electrical flow: your stock electrical wires is like getting water from your typical garden hose. Doing the Big Three with 0GA wires is like getting water from a fire truck's hose.
(Of course, unless you have an upgraded alternator doing the upgrade using 0GA is pointless.. for cars like yours, 4GA is fine)
Level Matching and Gain Controls
What level matching does is that it "normalizes" the music. Different speakers have different sensitivity ratings. For example, give a horn drive 20W of power and it'll scream at you. If you give a subwoofer 20W of power, it'd hardly move. But you're not an installer, so you shouldn't fret about this. Everything should have been done by your installer already *wink*