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You can turn fully invisible at will, photons pass right through you until you choose for them not to, but you also cannot see while invisible
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At any time, you can camouflage yourself with your surroundings. It takes 10 seconds to complete the camouflage, and in that time, or if you move, or if your background changes, you are visible. You can see. You can decamouflage at will too, which also takes 10 seconds.
In both cases, it is just your body which is affected, not anything you are wearing. Piercings or medical stick ons count as part of your body for these purposes.
In case 1, what will happen to the photons that my body emits, i.e. heat radiation?
You stop emitting photons while invisible. This does not have any unpleasant aide effects.