There's 3 kinds of power ratings, p2p (peak to peak) which sounds big but is useless as a number since it's the full range of the sine wave, not the + or - (depending on phase) which is used. That's peak, the 1/2 size full range of just + or - which is used. It's generally found in better components. Lastly is rms, which is the best rating, and only really found on high end components. It's the range on clear sound, anything over going into useless distortion. Pick one. Base all your components on just that, or the numbers will quickly get all screwed up.
3 ways to make a connection. Parallel is + to + and - to -, so a speaker lead goes from amp + to speaker + and amp - to speaker -. Speaker count doesn't matter, every + goes to the amp + in 1 line.
Series is different. That's amp + to speaker1 +, speaker1 - to speaker 2+ and so on, every speaker in line with the wire, not sideways.
Bridged. This is an amp setting,not a speaker connection. Bridged is mixing the 2x channels, so amp right + to speaker +, speaker - to amp left -.
These can be all mixed and matched depending on what you want to end up with. Most sub coils are 4ohm each. Run series, the coils add. Run parallel they divide. So a dual coil sub is identical to 2x single coil subs. It can be wired with both coils in series or parallel. Series would be 8ohm (4+4), parallel would be 2ohm (1/R = 1/R1 + 1/R2, or 1/½= 1/4 + 1/4). By bridging you cut ohm in half. You are only using half the resistance of either channel at any given time. So a 4ohm speaker bridged, the amp would see a 2ohm load. This gets tricky in cheaper amps that are only 2ohm stable and ppl slap 2x 4ohm subs in parallel or a dual voice coil sub wired parallel. You get a 2ohm resistance, bridged, so the amp sees only 1ohm at load, and burns up quickly, trips the thermal coupling, blows the fuse etc.
Kinda gotta know your subs. The 10w3v3 is 4ohm single coil rated at 300rms/600peak. The 10w3v3-2 is a 2ohm single coil rated at 500/1000. The 10w3v3-4 is a 4ohm single coil rated at 500/1000. All 3 versions work best at 150w-500w rms in a 0.625 cubic sealed box. (that's really small).
Now. You have a dual channel amp. With 2x subs. If the subs are 2ohm, they can be wired series and bridged, that's (2+2)/2, so the amp sees a 2ohm load. That's good. If the subs are 4ohm, you wire parallel for a 2ohm load. If you mess up and wire the 2ohm subs in parallel, that's 1ohm resistance /2 =0.5ohm on the amp, you'll cook it. If the subs are 4ohm, wired in series that's 8ohm resistance /2, so amp sees a 4 ohm load in bridge and while that's fine, it's the same volume as if you put each sub on its own channel.
So figuring out what you have, and how it's hooked up is best done on a piece of paper first.
Caps. 1/4 Farad for every 250w rms. Lead/gel batteries are slow to give up amperage and even slower to recover. So when you get a massive draw, like on every beat the base hits, the battery will dish out the amps, every light goes dim from the current loss, and if the beat is too fast, you'll start damaging stuff, especially the cells. Caps are almost instant battery equivalents. Your battery charges the cap, the amp sucks the cap dry, rinse and repeat. Recovery is next to no time as the battery isn't affected. This affects performance but only to the extent that it maintains the power output to the amp instead of loosing power when directly from the battery. It doesn't increase performance beyond the capabilities of what's there.
Ground. Shorter is better, should be less than 1 foot. Type of ground path is more important. There should be one. That means a good ground from battery to frame (full frame vehicles, amp grounded to the frame) or good ground to body in a sub-frame vehicle. Try not to rely on body tack-welds to supply a path back to the battery.
Wire should be slightly oversized for the job, and high conductor count. Electricity does not travel through wire, it travels on the surface. The more individual conductors, the bigger the surface area. The circumference of 2x2cm wires is greater than the circumference of a single 4cm wire, so that nice soft, flexible 1000 strand wire is far more effective at moving electricity than the cheaper, stiffer, 12 strand stuff Walmart sells.