Do film studio have to acquire rights for a public domain character or they can use them freely? I mean characters like Hercules, Thor, Social figures or fairy tale characters or any other religious/mythical characters. These character aren't owned by any studio or a person, so are film studio free to make TV series or movies on them or are they required to file copyright registration for them?
As MeatTrademark has alluded to in his comment, public domain works possess no tangible copyright from which licence fees can be extracted.
An author's intellectual property protection expires in most cases 70 years after publication (making it almost always outside their lifetime), however in the United States this has been somewhat dubiously extended to 95 years after first publication.
Sherlock Holmes is an interesting example, as since this amendment some of his work remains under copyright, and some doesn't. Looking at the details explains some of the nuances of IP law.
Conan Doyle died in 1930, publishing his last novel in 1927 (The Case-Book of Sherlock Holmes), meaning that particular work will stay under copyright in the States until 2023).
Conan Doyle's estate are notoriously litigious about enforcing this, and as such they will sue anyone whom they believe to be even alluding to the latter works. "The New Annotated Sherlock Holmes" is a recent example of this.
Furthermore, incarnations of a character can themselves be protected against reproduction within reasonable grounds. This very event happened when the BBC tried to take action against CBS for their 'co-incidental' re-imagining of Sherlock Holmes shortly after the announcement of Sherlock.
However, the general character of Sherlock Holmes is Public Domain, so new interpretations are legally unprosecutable. It is only remakes of remakes that muddy the water, as it is not Conan Doyle the newer work is adapting, but the remake itself (and authored within 70/95 years).
"The concept of a new Sherlock Holmes is unprotectable. But if the unusual elements of the BBC series – the modern settings, characters, clothes, plots and distinctive visual style – were closely reproduced in the CBS version, that could form the basis of a potential copyright claim.
However despite there being little opposition to the notion of Sherlock Holmes being Public Domain, The BBC, CBS and Guy Ritchie all chose to pay the Conan Doyle estate their fee to avoid potentially laborious legal fees intended only to slow production. Such is the effect of legal bullying.
Characters also require an identifiable author in order to create an estate that will act in its interests, so your other examples (Thor, Hercules) do not fall under any estate's remit. Most fairly tales are cautionary tales that have been in circulation for hundreds of years, and surface in different cultures in different ways, demonstrating their universality.