Water, algae, forest, trees plants, atmospheric circulation, crops.

No, it won't. That is, so long as life and the Environment continue as they have been.

The Earth and the Atmosphere are not a closed system. Like being locked in an air-tight closet and having only a limited am amount of oxygen available to you, which you are depleting with every breath you take.

No. The livable part of the atmosphere is called the Biosphere. And it is a dynamic, cycling, growing and evolving thing. Oxygen is continually provided by plants and other flora, which take in carbon dioxide and then give-off oxygen. So we should all be good to go as this process continues.

But, one caveat to this rule, to the OP question of us running out of oxygen, would be if some catastrophic occurrence happened. An airborne disease that killed much of the plant life. Or, say, an asteroid strike like the one that wiped-out the dinosaurs 65 MYA. That one raised such a storm of dust and debris and smoke and fire that it basically suffocated everything. Blocking out sunlight so the plants all died, thus derailing the oxygen supply.

Plants are able to take in gases to produce oxygen.So long as the sun exists,there will be an unlimited supply of oxygen.

It's not like oxygen is gonna leave Earth. How would you suppose that oxygen leaves the Earths atmosphere?