Are junk DNA's mb also counted when it is stated that human DNA contains 3mb?

non-coding, information-rich, DNA

Since noncoding DNA contains many long repeating sequences repeated thousands or even millions of times, it is not necessarily information rich, and is often extremely low entropy.

Does human DNA contain that much (the most) non-coding parts?

No. The human genome is a midsized genome by eukaryotic standards, so it's not going to contain the most of almost anything because it isn't large enough. To put into context, the wheat genome has ~6 times as much noncoding DNA as the entire human genome. Then there is the lungfish, which could fit as many again copies of the wheat genome into it's noncoding DNA:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5718017/#Sec1title

Could it be that this huge amount is what makes us "free"? That thát's the reason why we differ from other species in an obvious way?

Our genomes are very average for eukaryotes, so not likely.

Has there any research been done to answer my claim?

Yes. The puzzling lack of correlation between genome size and organism complexity was an unsolved mystery in biology for about half a century. It was eventually resolved when high throughput sequencing combines with bioinformatics revealed that the actual information required to build an organism is very low compared to the typical size of a genome, and so factors other than information content drive genome size.

Also as an aside since I saw this in the comments: since a BP can have 4 values, it can store 2 (not 1) bits of information. Most BPs store less however because they are not random.