Seems like way too many exercises per day. You could use less exercises per day. If you still want to keep them all, you could have a rotation. Like Chest/Sh/Tris A and Chest/Sh/Tris B.
The body can withstand more than most people think, especially if you supply adequate nutrition. If you feel that you are overtraining, (joints hurting, terrible performance in gym, lack of energy or...
That doesn't change the fact that it's a crappy setup. It would be easier if you would attend a real gym, with power racks, more barbells, area, dumbbells, and space period.. I'm sure you can go out...
Get that gym membership, that is the only true way to ensure that you have enough equipment to follow you as you progress. Unless you want to dish out the money yourself for a good setup, of course....
How many sets, exercises, and reps do you do on your training days? You're lifting 6 days in a row...with an upper lower split, that's hitting your muscles 3 times a week....
The best "fat burning supplement" is a good weightlifting program with some cardio along with a good diet. A fat burning supplement will do little good for you until you already have all those in...
We need more info. Post up some stats: measurements, max lifts (real ones not inflated, be honest), prior training experience, weekly schedule for lifting, injuries...
You seem eager, and that's good. You're going to have to put in a lot of hard work and a lot of food if you want to gain a lot of strength and muscle. Spend your money on creatine, multivitamins,...