Hey vignes,
first of all great that you started working out! with 14 i spent time in front of my pc playing call of duty:-D i prefer your choice!
1) the rest days are very important my friend, your body do not adapt without enough rest time. that means no muscle growing if you give your body not the chance. i would recommend you doing the cardio routine on the same day, but maybe in the evening, so you split up your workout. if you do not have enough time, do it on the rest days, but not on everyone. for example a week could look like:
day1: training
day2: cardio
day3:training
day4:rest
day5:training
day6:cardio
day7:training
day8: rest
at least try to find some rest days!
2) of course you can do the full body workout after waking up without breakfast, but the question is why? do you want to lose some fat? if not, i would recommend you to have a good breakfast, it supports with the energy you need for your workout. please give an answer than i would like to give you a detailed text back about the pros and cons of working out with nothing eaten before :-) but for that, you should inform us about your goals