Usually when I return home after my tasks, I have only half an hour left if I want to get to gym ion time.

To be "on time" is to be punctual; to arrive at the correct designated time, which works for habits too if you habitually go to the gym at the same time every day.
"In time" tends to need a complement and wouldn't be related to something that has a clear start time. It's often used when it's lucky/fortunate that the person is "in time" for something.

Some examples:
"He will be fired because he is never on time for work."
"You are just in time to see my finished drawing!"

In the time iI have left i, I basically just eat a lunch and then go to clean myself by takingake a short, simple shower.

I would add "just" here as we often do for emphasis (in this case, emphasizing not doing a lot because you don't have time). When saying you are going to shower (or take a bath), you don't need to add "to clean myself" as it is understood and would be redundant.

Choosing ato shower instead of taking a bath is more efficient to get yourself clean igiven my time condition, becuause it's literally help you rinse off quickly by being washed under flowing wather what causes time saving and alsoyou can rinse off quickly. It also saves time and wastes less water, and. Plus, for me it is pretty clear that taking a bath isn't an even option.

We'd be more likely to speak about choosing between the two activities (showering and taking a bath) instead of choosing the two objects (a shower or a bath tub).
You can use "given" when explaining reasoning within a certain situation: Given that there's a storm today, it's a bad time for a picnic.
I made some general edits for clarity.

BTaking a bath is a waste a lot of time and water. You have to fill the allwhole bath and even though youtub and you actually need to rinse off yourself off harder for a reason thatbecause the bath water isn't the same as shower wather that's, which actually comes from above and flows the showerhead andto rinses off the soap.

The bath isBaths are more for a personpeople who seek relaxation to heal from all the tirednessfatigue and the tension they experienced, which is called meditation.

Slightly more natural to speak about "baths" in general as opposed to "the bath."
Fatigue = tiredness ; it is a bit more eloquent

The more we learn how to buse/waste less water waster, we are devleopi, the more we streng then habit ofs to savinge our/the planet.

Our planet won't be able to provide moreenough wather in this rhythmwith our current practices of always wasting water, s. So please, wellhile you still can, try to think a bit and (do your part to) help to save our world by simple smallwith this small, simple habit.

The part in parentheses is optional, but would often be used in cases like this, where we are speaking about doing something individually as part of a larger social goal.

Besides, taking a shower before going to the gym makes me feel more refreshed and ready for my training.