Confusion over music library

I had built up a music library on my MacBook Pro - some songs were taken from CD's, some were purchased from the iTunes Store. I have all these songs on my iPod Touch. I haven't joined Apple Music.

I got an iPhone SE a few months ago. I happened to go to my music library on the iPhone and none of the songs are there - they all show the cloud symbol to the right of the song title. I don't recall if that's just the first time I noticed this or whether it's been like that since I got the phone because I mainly used the iPod for music. I would like them to be on the phone. I know I can download each song one at a time, which is all I could find in searching about this, but that would take a ridiculously long time. Is there a way to download all purchased songs at once?

Also, what about the songs that weren't purchased but were in my iPod library? Ideally what I'd like to do is initialize the cloud music information, move everything in my iPod or MacBook Pro music library to the cloud and then move it down to the iPhone. Is that possible?

Thanks.