iPhone Mystery Music

I have an iPhone 5S and MacBook Pro. I have two problems (which I believe are separate?!?).

1) I have songs which are clearly in the Music app on my iPhone which do not appear on the listings for my iPhone when the device is synced to my Mac. In fact, I have never asked for these songs to be transferred from iTunes on the Mac to my iPhone. I was unaware of this until I asked 'Siri' to play all songs (shuffled) and some of them came up. With the iPhone plugged in via USB to the Mac, these songs do not show on the list of what should be on my iPhone, nor will they appear after a search of the iPhone's music through the iTunes search facility. If I can't find them, I can't delete them. They do appear when searched via the home screen swipe down search feature on the iPhone. I don't know how many of these phantom songs are using up precious memory, nor how to delete them and stop such a thing happening again!

2) Every time I sync the iPhone to the Mac, songs appear 'greyed out' and will persistnently re-appear no matter how many times I keep deleting them via iTunes. This is not connected, I believe, to the 'Show all music' feature on the phone which has been switched off. Also, thses tracks do not have the iCloud symbol next to them, such as when you set the 'Show all music' feature on. For example, I bought the latest Elbow album and after a few listens decided that I only liked half the songs and deleted the rest. Each sync, the deleted tracks appear ib the list of songs which the iTunes (on the Mac) says are in the phone.

There are an ever increasing number of these and it is getting annoyoing. I am also suspicious that this too is taking up iPhone memory.

Thanks,

Dolbinator