No.
Burning fat into muscle is a myth.
However it is possible to loose weight and gain muscle.
Whoever told you not to eat was a liar.
What you put in your body is what you get out in your workout. Have around 6 small ( less than 300ish) calories a day to keep you full of energy and drink LOTS of water.
Gz on the 10KG
I saw your routine.
1) Monday Wednesday Upperbody day ( Hit pullups, dips, tricep pushdowns, Bench, and do some pushups on the side man.)
DONT FORGET TO TRAIN YOUR NECK CORRECTLY
Do some bridges or go on a bench and tie a 5lb around your neck and move your head side to side and up and down.
2) Tuesday, Thursday Lowerbody day( DEADLIFT!!!!!!! Squat till your ass hit's the deck, Leg press, Grab a 45 and go over to the glute and ham machine drop the plate on floor and lift that shit and your whole body. You'll feel this in your ass and be sore.
3)Friday, AB DAY!
Crunches, flutterkicks, go to the tricep pushdown, get on all fours then grab the rope and start pulling it down with your head facing the floor. Trust me it works.
Get some gains.