That is false. You don't need NSO for f2p online games.
And why do so many people have issues with the cloud saves? I got a new Switch last year and had no issue transfering over 150 games to the new Switch. Only Splatoon 2 required me to transfer the save file manualy, but it only took like 10 minutes.
Wasn't sure. I know Sony always had free to play games available with no extra cost and Microsoft just started the policy this year. I had Switch Online since the beginning and when it lapsed, I couldn't even go to RE.Net without the subscription. It's good that they're customer friendly in that regard. A lot of the most popular online games are free to play.
I have probably 60 games but I haven't really tried to transfer many of them. I rarely play the Switch Lite. It usually works pretty well but for some reason, Bayonetta 1 didn't cross. It says it's backed up on the primary switch but the second one doesn't recognize it.