Cuticle Away...this is CND brand isn't it?
If you are using Cuticle Away, this must be deactivated with water, if you are not doing this, then the nail enhancement will not adhere to the nail, no matter what you do.
After you have filed the nail, I would use the Plush Brush to wipe away and dust and then use Cleanse to ensure the nail surface is clean.
Then use Nail Pure and make sure you give the nails a good rub with the pad soaked in nail Pure.
Also, make sure you don't drown the nail with primer, just a small amount is needed.
Make sure you really pat the L&P onto the nail to make sure it is well attached to the nail.
Try using a very slightly wetter mix ratio for the colors and glitters but ensure the product does not touch any surrounding skin.
In regards to the friends nail that just popped off, this just simply does not happen if the nail was attached properly, so in that situation, there was something that went astray with your application process and my bet is on the Cuticle Away and not correctly removing it, if this is what you actually used.