To start off you can take it a little easy with the running, Stretching before lifting is important, make sure your body is warmed up before you lift.
Lifting every other day, you can do it everyday as long as you make sure you do not repeat the same muscle groups everyday and give them a days rest atleast.
Since you want to cut, you should make sure you have a good diet with a good amount of protein, especially if you are under weight. Gaining mass and then cutting is the way to do it but it is not a short process. In that case you can start of with lower reps.
Reps, yes reps count in everything, so no need to do high weights and low reps unless size is the only thing you want.
But Keep a good number of reps and a standard of 3 sets.
Starting of, you want to make sure you dont over do it for the first few weeks until your body is warm and in the routine.
Once you feel comfortable with a certain weight go ahead and try the next step up.
You dont want to under do it either, so go give them a try atleast.
About the Cardio, yes it is good to burn fat, but you do not want to loose all your energy before you even start lifting.
Cardio after working out is good since your body has already used up its energy and that is when you start to burn fat. No Cardio 6 days a week is not dangerous, as long as you dont over do it.
As mentioned above, a good diet is important so you might consider taking in food from home. Anything from Tuna, chicken, Fish etc. You will eventually need to get yourself protein powder as you advance.
For the time, just make sure you have eaten before hand and as long as your not stressed out and tired.
Weight lifters in general have stomachs, but you should be good as long as you work on your stomach and have cardio in your exercise.
Make sure you take your measurements before hand so you can notice improvements and work on your weak spots.
It will be atleast 1-2 months before you start to notice considerable change.
Go ahead and try and be consistent,
Good Luck.