Those power wires would be perfect.
The end that goes into the amp could/should be bare (raw wire). The other end(s) need to terminate onto the battery positive and the car chassis negative ground post.
You'll also need a fuse and fuse holder. For the money; you're better-off just buying a whole kit, and not using the extra speaker wire:
Kolossus Fleks 4 Gauge Amplifier Installation Kit - Merchandise
Yes, you will need a few sets of RCA's... Stinger 9000's are really nice (if you want to spend a lot of money).
There are lots of options for RCA cables, and honestly; a cheap pair will work just as good as an expensive pair...
As mentioned by another member; the Stinger 8000 is really good too (it's what I use). But Knuconceptz also makes decent ones at a good price.
www.knukonceptz.com
Do you have a jigsaw? It's fairly easy to take out your OEM speaker and trace it onto a piece of 3/4" HDPE, and cut them out yourself.
You can get HDPE on Amazon:
Amazon.com: HDPE (High Density Polyethylene) Sheet, Opaque Off-White, Standard Tolerance, ASTM D4976-245, 0.750" Thickness, 12" Width, 24" Length: Industrial & Scientific
www.amazon.com
If you're not comfortable doing this yourself, then there are guys that fabricate these (I just don't really know who they are).
Here's an example:
Online Shopping at a cheapest price for Automotive, Phones & Accessories, Computers & Electronics, Fashion, Beauty & Health, Home & Garden, Toys & Sports, Weddings & Events and more; just about anything else Enjoy ✓Free Shipping Worldwide! ✓Limited Time Sale ✓Easy Return.
www.aliexpress.com
The LC7i is not even in the same league as the SDMI25. The SDMI25 is a SUBSTANTIALLY better option, and to be honest; the SDMI25 is easier to install.
The LC7i is just going to tap into your existing speaker output. And that signal is going to be garbage.
Trust me. You'll spend your whole life trying to tune-out the factory EQing.
The SDMI25 goes straight to the source, and gives you a pure clean flat digital output signal.
For BMW; the Helix SDMI25 is the absolute way to go.