Definitely! I have buffed out much worse. You might need to start with 1500 grit sand paper or even 800 or 1000 grit if there are deep scratches in the sides.
The bottom just looks like it needs a good cleaning. I would put a gallon of vinegar and 5 gallons of water (or more water to give you 6" or so) in the bottom and let it sit for several days. You can put a pump or powerhead in the bottom of the tank with the vinegar and water which will speed up dissolving the calcium deposits. You can also put a submersible heater in there with the pump to speed things up. Heat and circulation help dissolve the deposits faster. Scrub the deposits once a day to dislodge the softened surface stuff and expose the lower deposits for the vinegar to attack.
I have never seen a reason to have the bottom perfectly clear and buffed out to a fine degree, it just gets covered with media anyway.
A heavy vinegar concentration can burn your skin so you might want to wear some kitchen gloves.