I would not use carpet under the stand, if it gets wet it will hold the moisture, an you will have a mold problem. you could go to Hd. or Lowes and get a sheet liner for a shower stall basen. I think it's about $10.00 afoot, and it's 5 ft. wide.
Yes it is hair algae. You need to stop using filtered tap water and start using RO water You may also want to add more water flow by add 2 small power heads
You may need more flow rate, I added 2 powerheads Rio 600's I put them on PVC pipe Cut the bottom at 45 and send the water down to the bottom of the tank, you can get a big endcap to set them in, to keep your sand from blowing around