What would be a good recording app for either apple or android where I could, say import a backing track and record myself playing over it?
Yep Garageband works great for this. Literally open itunes and drag n drop any song onto an open track. Ready to go.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY