20 ft. Indoor LED Soft White Tape Light

This particular item does not come with a remote, or even a power supply, only the light strip and some connectors. So it depends on what remote and receiver that you buy to add on to this.

Hi Mort, Please note this item does not come with power adapter. You would have to purchase it separately. If you need to do the 3 measurements you are asking independently, you would need 4 kits. Once you cut the strip to size, the remaining piece cannot be reconnected. You would need 1 for the 6ft, another for the 12 ft and 2 kits for the 32 ft allowing you to cut the second strip to the 12 ft you need to create 32 ft. The 32 ft will work with the adapter. Here is a link to the power adapter you need: https://www.homedepot.com/p/Commercial-Electric-60-Watt-12-Volt-LED-Lighting-Power-Supply-with-Dimmer-17065/207018576

This item is ONLY the tape light, no remote dimmer or transformer is included with it.

No. Once it is cut, you are unable to connect it back together. This one may be better for what you are trying to do. https://www.homedepot.com/p/Commercial-Electric-12-in-30-cm-Linkable-Single-Color-Indoor-LED-Flexible-Tape-Light-Kit-4-Strip-Pack-17066/207018583 It comes with connectors making it easier to go around corners without cutting.

The power source is a separate item and installed in a different location

The one you are looking at is 12 volt, the other is 24v, so no, even though the power supply is rated for 48 feet. Read the data sheet

Yes, you can cut it at the designated spots and use the connectors to re attach. Actually it is pretty easy to do

Each will need transformer/power supply.

It's perfect for those led.

Yes for both but require different power supplies.