I can no longer play my songs consecutively on my iphone
Apple has updated the music app. The icon changed with the update in iOS 7, I believe, and the music app saw some big changes with iOS 8.4. Some of the UI is harder for me to figure out and use but all of the old functionality should still be there. 

To play an entire playlist, tap the Play icon in the upper right of the playlist. It should be overlaid onto album artwork (likely of 4 albums). 

To have continuous repeat, after starting the playlist, tap the bar just above the navigation bar to see "Now Playing". Then, at the bottom (you may need to scroll down) there are standard icons for repeat and shuffle. If the repeat icon in the lower right had a "1" next to it, it is set to Repeat 1. Tap the icon to change it. 

You can find more information about the new Music app here:
http://m.imore.com/how-use-new-music-app-iphone-and-ipad-ultimate-guide