WS2812 type strips operate on 5V, and have individually programmable LEDs. They can take a lot of current though. 1m at 60LEDs with all 3 colors fully bright takes 3.6A. For indoor use you can probably run them at 10 to 20% of that current through, and you will not have all of them on all of the time.
Yes you can. It does PWM with 8 bits for each LED. If you make the 8 byte 11111111 you are using 20mA. If you make it 0111111 then you are using about 10mA average current. If you use 0001000 you are using about 1.25mA average current.
Ws2812b led strip with arduino nano and fastled library. This library knows if the battery current exceeds its maximum and changes the program accordingly.
It's used very often for wearables that need to be portable and battery operated.