Electrical – power seven 54W LED light strips from a 400W supply

I'm not familiar what that product specifically, but the "amplifier" in this type of lighting setup generally only reads the input from the previous upstream light strip and provides power from its power source. Therefore, the amplifier draws no current from the upstream lights.

Instead of 2 power supplies, you could use one power supply larger enough to satisfy all of your power needs.

To answer your questions specifically:

1. Yes.
2. No. Power supplies are rated for the current that they CAN deliver. Using a power supply larger than needed is fine.
3. Again, not knowing these devices specifically, I am going to guess no based on my experience with other, similar products.
4. Generally no, provided you do not draw more power than the supply is rated for.

The power rating of the supply must be higher than the power rating of the load -- so based on the numbers, yes, this seems sensible.

However, the strip lights themselves will not support running that much current through them -- which means you can't just daisy-chain all the strips lights.

From https://www.pololu.com/product/2547:

• The 60 LED 1 m strip drew 3.0 A and had a voltage drop of 0.6 V.
• The 120 LED 2 m strip drew 4.7 A and had a voltage drop of 1.4 V.

The voltage drop means you'll have dimmer LEDs.. and at some point they'll stop working entirely. To get around this, you should provide power to each strip. You can interconnect the data lines, but separate power wires should be run to each segment. How long the segments are really depends on how much voltage drop you can tolerate (how dim the LEDs at the end get).

You can use a voltage drop calculator (Google it) to figure out the size of wire you should use for the distance and power draw -- but expect to probably run 18 or 16awg wire from your power supply to the segment.

It may also make sense to use multiple smaller power supplies (with shorter runs), depending on your distances, room layout, etc.