Multiple LED’s, one controller, diagram included

These strips are usually arranged in numerous parallel segments of a few series LEDs. The RGB strips can be a little different, but they work basically the same way. It looks like your strip is analog control and not digital (which would have little ICs in the strip to control individual LED color), so the specific color ground lines are all in parallel. You should be able to connect numerous strips in parallel - 12V to 12V, red to red, green to green, and blue to blue to blue. That is the same reason you can cut the strips into smaller segments if you want.

There is a limit to how much current can flow through the strip itself, which varies between manufacturers. Your other limit to how many strips can be connected together is how much power your supply / remote controller can handle. It should specify a limit in watts / current or total number of LEDs or parallel segments. That information should be on a sticker on the power supply or be listed in the manual.

From your product page:

Power 72 W

Which is 6A at 12V DC. That means your power supply/controller has to be able to handle at least 144 W (12A @ 12V DC) to connect two strips in parallel. Although, it is never a good idea to run something long term near its maximum ratings, so the supply should really be rated for something closer to 200 W.

If you are able to power multiple strips from your supply, it would be best to power them with a star topology so the current for each strip is separated. For example, connecting Christmas lights together end to end is daisy chaining, and the current for every light strand has to flow through the strands before it. Powering multiple light strands from one power strip is more of a star topology, with the current to each strip only flowing through itself (think of the power strip as your power supply).

Dumb RGB LED strips like you have are simple. Each segment consists of 3 channels. Each channel has 3 diodes and 1 resistor in series. Each segment is in parallel with each other. Cutting and extending the sections with wire does not change that. You will not experience an increase in current because of it (in fact, extending with wire will actually cause a decrease in current, due to the non-zero resistance of the wire. For your short runs, this is negligable).

That said, adding 100 segments, each with 3 ~20mA channels (so 20mA x 3 x 100 = 6 Amps!) To the dome circuit of your car will A, cause the fuse to blow, probably, and B, cause a fire as wiring for the dome light is not sized for multiple amps. A relay in line with the dome switched circuit, to a new fused circuit (or the cig circuit, that's normally fused for 10 Amps) is the safe approach.

Update: a 1.5 Amp controller will not work well with a full 300 led/5 meter length of rgb led strips... At most you can power 25 segments! Thats 500mA per channel/color