Connecting Multiple Strips (Fuses, Wire Guage, and Capacitors)

Sorry if this is a little long. I’ve done a good bit of reading on fuses, amps, etc. but am still a little unclear and just want to confirm that I’m wiring everything safely.

I’m connecting three LED strips (SK6812 x 144, ~9A draw each) to a power supply (5V 40A). The three strips run parallel to each other so I’m going to connect all three directly to the PS as well as running two cables to the two mid points for power injection.

Could someone tell me if what I have below is okay?

Based on the calculations from https://wled-calculator.github.io/, the power injection wires should be 16AWG, each with a 7.5A fuse. That seems reasonable as these two wires together will theoretically power 1/2 of the LEDs or 13.5A.

What about the other ends of the strips that connect directly to the PS? The calculator recommends 4A fuses, but 4A x 3 is only 12A. I was tempted to think that since these wires are very short (5-10 cm) I could omit the fuses. But I’m guessing they’re needed as a fail-safe in case the injection wires ever become disconnected.

Also, I’m looking at fuse holders and just want to be sure. Provided your below the max, are fuses not volt specific? i.e. Do I just have to worry about matching the amperage?

And my final question is about the 100uF capacitor recommended in most wiring diagrams. Since there will be 5 wire pairs from the PS to the LED, do I put one on each? or just on one pair, and if so which? (And for what it’s worth, the LED controller will be wired separately - i.e. a 6th connection to the PS)

Thanks!