Background insulin is your levemir. That's your long acting basal insulin. The job of the basal insulin is to keep your blood sugar flat when you don't have any fast acting insulin in play, you aren't taking in any carbohydrates and you aren't doing any unusual exercise.
Here's some info on basal testing -
https://mysugr.com/basal-rate-testing/
It does strike me as unusual to hear 90% of patients at your diabetic clinic are on metformin, unless that includes all the type 2 patients too.
It's not that unusual for a type 1 to be on metformin, but it's certainly not the default position. Reasons a type 1 might be on metformin include: insulin resistance; dawn phenomenon; type 1 ladies with PCOS wanting to get pregnant.
It does sound like DAFNE would be worth completing for you - it could help you understand how the basal bolus regime works and then, hopefully, how to make it work for you.
As a starting point, there is a free carb counting course available online -
http://www.bdec-e-learning.com