Eh, no. Mathematics is an hallucination of ours we are trying to desperately map onto reality. I say this as a mathematician. When you look out into our reality, you know what we see? A curved universe. There is nothing in our reality that is truely STRAIGHT.

YET, we creatures came up with such an unnatural thing as a straight line. Straight lines are a uniquely human hallucination. Its the logic we use to make sense of the world, but its a Rorschach test of our own making. You are attaching meaning to it because thats what our brains do. generate meaning out of chaos.

I need to look no further than pi, which is a number that represents our feeble attempts to push the round universe into our square heads. Its trying to represent the curved universe as a straight line (and visavers) - and reality said : LOL, NOPE!! YOU get a number that is more illusive than the irrationals. A never ending non patterned number.

All of nature is not based on mathematics. Mathematics is the language we use to describe nature. Thats like saying the Grand Canyon is BASED on book describing the Grand Canyon.

1.) No its not. Its our language, not nature's.

2.) To a degree, yes. But thats because our brains are pattern seeking and pattern generating machines - not because nature follows a system WE made up.

3.) Did I mention Pi yet

Here

https://i.imgur.com/a5ueCi5.jpg

THIS is a graph of a discovery that I made in number theory. Does it look like it has a pattern to you? I think this is the most beautiful thing I've ever seen, because IT MAKES NO SENSE. which means, we still have a lot to discover and learn

mathematics is a human language/system.

nature just follows the laws and quirks this universe has. the plants, animals and subatomic particles will keep doing the same, regardless if we have a tool or theory that can describe what they're doing.

sure, there are patterns everywhere in nature, but i would not go as far as to say that that makes mathematics a language of nature.

I would say there is no language of nature; there are things that happen, and we can approximate what happens using math. Math can be used to describe basically anything, so the fact that we can understand these things through numbers is not extraordinary.