Yeah, you can cut it to size. They'll still work the same, maybe a bit brighter thugho. If you wanna connect the rest of what you cut off you'd need to solder it to the rest of the strip connected to the power supply. The warm white and cool white are both full spectrum, but unless this is for a veg only tent, you definitely want the warm whites.
and this LEDJump Under Kitchen Cabinets Bright LED Lights Lighting Dimmable 12V Volts, 3M Adhesive Tape, 16FT/5Meters Include Power Supply (High Power Warm White 2500K-2700K + 60 Watt Power is one that would work?
If you wanna connect the rest of what you cut off you'd need to solder it to the rest of the strip connected to the power supply.
The warm white and cool white are both full spectrum, but unless this is for a veg only tent, you definitely want the warm whites.