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Since the beginning of the year the goal I set for myself was to dedicate myself to strength training to build muscle.
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I've definitely been increasing how much weight I do for each exercise about every two weeks or until I can comfortably do 4 sets with 10 reps each.
These two quotes are contradicting each other. The 8-12 rep range is typically considered hypertrophy work, while 1-5 reps is considered strength work. A strength program will also typically have you following a full body program, not anything like a 5 day split per muscle group.
An actual strength program might get you to your goals even faster.

Search 'Stronglifts' or 'Starting Strength'.
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Skip the cardio and you'll be better off...
I'm serious.
I agree with this, but for a different reason. Any other exercise besides strength training (and what Big Bad Wolf suggested wasn't strength training, it seems like you'd be going quite a bit higher than the 1-5 rep range) will limit your strength gains. It will help keep fat off, sure, but I'm a fan of bulk/cut cycles and as such believe strength should be your #1 priority at this stage, and not worry about fat (within reason, of course).
In any case, cut the cardio.
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2 "sets" to FAILURE 10 reps , 12 reps mean nothing momentary muscular failures is what you need,
Going to muscular failure every set hinders steady progression. You'll make more gains from that workout, but not overall.
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if you gonna use movement go slow 5 second positive 5 second static hold 5-10 second negative if ROM permits,
RVAIS, we discussed this in another thread. Lifting slowly performs equal work but makes you LESS powerful. Plus it lets you lift less weight. There's really no good reason to be lifting slowly. Lift steadily (keep your form in check) but feel free to lift as fast as that permits.
I disagree with your sentiment that you should rest until 'fully recovered'. A person training 3x a week with only partial recovery each time (a day or two is sufficient for most of the growth to occur) will make better gains than a person training 1x a week with full recovery (since in the extra days they're waiting, they're gaining less per day than the person who has trained again).
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. you should improve every workout or dont train.
Amen.