1. That's not true, It takes more 'arm' to cast single hand and it won't cast as far as a big spey rod will, but a smaller lighter spey rod won't cast as far as a big spey rod either. They are a just a two hand rod that is not big. The term switch rod was invented by Bob Meiser when he developed a line of small two hand rods.
2. Is a complete load of hogwash. There was a guy on here who posted that a bunch of times, but he was wrong. I land fish by hand by myself all the time with 15' rods.
3. That's not right either. I don't like Scandi or Skagit so I never use those lines. Scandi is a style of casting and it uses faster rods and shorter heads. Skagit is a type of line and has a number of different tips and cheaters. A wallet is more like what you would need if you went that way. I top hand cast because I can get way more distance and use much longer heads.
4. is completely wrong also. In fact if you are going to use a two hander in the surf, the switch rod is the least capable rod in the bunch. I'd go as big as I could because the ocean is big and a far cast is never to far in that case.
now for the questions
1. No, just make a stripping basket and do just like you would with a single hand rod. That's how I do it and I'm casting in the 140' range all of the time.
2. As I said, a full on Spey rod would be better for the surf but it would work, the Trinity I'm pretty sure gets it's fair share of guys with switch rods.
3. The idea of a switch rod is to SPEY cast, not roll. It would be like using a Ferrari to take the kid to school. You can do it, but seriously, why?
4. You can use a floating line on any switch rod. The rod does not care if your line floats or sinks, just what it weighs.
One last thing. I am not a huge fan of the casting instructor. I taught myself with you tube videos. It is not rocket science. It's easier to learn than single hand casting. Also, if you want to get real distance, Scandi and Skagit are not the way to do it.