LED strip segments Parallel vs Serial
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