Drywall – What the white part is on the ceiling in this tutorial

As with many textures, it is likely formed from water-soluble base like drywall topcoat. If so, spray it with water from a spray bottle until you think it's saturated enough then take a wide drywall knife and see if you ca scrape it off. If this works, you'll need to tape and re-texture afterwards.

Alternatively, a drywaller can skimcoat over the top of it, then re-texture to your liking. They may often use a giant heavy-nap roller of sorts and "paint" on drywall mud. Then they scrape it flat enough to base whatever texture you intend.

If you could manually scrape off the large peaks before this, though, it will work better.

I'm sorry to say, and hate to criticize other's work, but those screws are not driven properly. The screws need to be driven with a sheetrock screw gun or a dimpler bit in a regular screw gun. The screws need to be slightly counter sunk with an indented dimple around the screw head into the sheetrock to hold some joint compound. The screws should not break through the paper. The proper bit indents and stops driving the screw at the right depth automatically. What I see in your pics is badly torn surface paper with shards of paper higher than the rest of the surface. This will be hard to mud and make flush and smooth. Many of these are going to have to be indented with a strike from a hammer to create a void for the mud to go into. The other problem with driving drywall screws with a regular #2 phillips bit is that screws driven too deep will not have the holding power and the sheetrock screws will pull through, leaving the sheet unattached to the studs. This is especially important when hanging rock on ceilings.

These are the proper tools and bits.

Be careful using Angies List, many of the reviews are fake and made by the contractor themselves. Personally check local references with a phone call or sometimes with a visit to see finished projects. I know that many of my customers are happy to talk to my potential customers and also proud to show off there new completed projects.