Fix with drywall compound or tear out drywall?

After reading some stuff online and asking a lowes associate I was told spackle would be the best option. Now i'm having second thoughts based on more readings. While destroying a fireplace mantel some of the drywall got destroyed/broken so I replaced with hardiboard. Made sure the gaps were very small I couldn't fit my flathead screwdriver in past the tip basically. I applied tape and put on spackle compound letting it stay overnight. Tommorow I plan on sanding it to an even surface till I can barely see the tape and apply a second coat followed by waiting 24hrs and then apply a third and final coat to make the wall smooth enough for me to apply tile onto it. Should I rip the tape/spackle off that i've already put on and apply joint compound instead? Should I apply joint compound on top of the first coat? Confused now after reading everything online need some guidance. Cliffnotes: Applied new hardiboard for tile area taped and put spackle. Wondering what is next step to make sure level for tile to go onto.

Hello there, I am a novice DIYer and have only done drywall once in my garage. Every time I have seen people hanging drywall it was in to wood that was typically 1 1/2 inch thick. That was how it was in my garage so it was easy to hang the drywall as the was enough space on the wood to screw in the edge of 2 connecting pieces of drywall. In my basement however, there is something I have never seen and I am not sure about. There I have metal in place to where the more usual 2x4 wood beams would be. These beams are only 1 1/4 inch wide and very thin so I am not sure if you are supposed to screw the drywall into them, or if the basement should be framed with wood... One of my friends said I can hang the drywall right on there but it seems too thin and flimsy to support it. Please take a look at these pictures. What is the purpose of these thin metal studs/strips? Can I drywall on them or does the basement need to be framed? Thank you.