The question says:
Callahan used torture to get the location of the hostage out of the suspect, and information acquired by torture is not admissible as evidence.
In general, evidence obtained by torture is indeed not admissible in US courts. This is particularly true when the person doing the torture is a police officer. If it is done by a private citizen, with no prompting or encouragement by the police or any part of the government, different rules may apply.
See Brown v. Mississippi, 297 U.S. 278 (1936) for the inadmissibility of confessions obtained through torture or physical coercion. The Mapp decision, cited below, would have extended this to information or evidence obtained via torture.
The question asks:
It was not merely information what Callahan acquired, but the physical body of the victim. Doesn't that change anything?
No. If the evidence was obtained unlawfully, then the evidence so obtained and all other evidence or information indirectly obtained through the unlawful act is inadmissible. This is the "Fruit of the poisonous tree" doctrine. It applies just as much to physical evidence as to a confession. "Fruit of the poisonous tree" doctrine is an extension of the "exclusionary rule" and like the basic rule, is intended to deter unlawful actions on the part of law enforcement and government generally, and to ensure that the courts are not complicit in such unlawful actions. The rule was first fully established in US Federal courts in Weeks v. United States, 232 U.S. 383 (1914) although versions of the rule go back before the founding of the United States. The rule was applied to the states in Mapp v. Ohio, 367 U.S. 643 (1961) although some states applied a version of the rule even before the Weeks decision.
There are exceptions, however, notably "inevitable discovery". That means if other, lawful, investigations already underway would certainly have uncovered the same evidence, then it may be admissible. Another similar exception is the "Independent source doctrine". This says that when the same evidence is later obtained independently from activities untainted by the initial illegality, it may be admissible. See Nix v. Williams, 467 U.S. 431 (1984), for both of these exceptions. There is also a good-faith exception where a warrant was obtained on invalid grounds but used in good-faith by offers who thought it valid.
I do not see that any of these exceptions would apply in the situation described in the question.
It does not matter how "clear" the evidence may be. If it is obtained unlawfully, and no exception applies, it will not be admissible.
The question asks:
In case of the hideout and the rifle, is such a clear evidence still inadmissible? Can't the "hot pursuit" rules be applied? He didn't have time for a warrant, he was running against the clock.
The doctrine of"hot pursuit" alone does not justify entering a private dwelling without a warrant, but there are a number of exceptions to the warrant requirement, one of which "Exigent Circumstances" is one, or rather a group of relates exceptions.
In Missouri v. McNeely, 569 U.S. 141 (2013), the Supreme Court wrote in its opinion, "A variety of circumstances may give rise to an exigency sufficient to justify a warrantless search, including law enforcement's need to provide emergency assistance to an occupant of a home . . . engage in “hot pursuit” of a fleeing suspect . . . or enter a burning building to put out a fire and investigate its cause."
Thus “hot pursuit” can be an exigent Circumstance and justify a warrentless entry, but this will depend on the precise facts of the case. It is not clear that the circumstances described in the question would qualify.
The question asks:
even if they decide not to press charges because they are afraid they can't win the trial, can't they at least put the suspect under surveillance?
Legally, they probably can. Not even probable cause is required to continue an investigation, or to place a suspected criminal under surveillance There might be reasons other than the law of evidence not to use surveillance, for example if the police fear that the suspect will observe the surveillance and thus be alerted. But this seems like a place where the movie plot may have been unrealistic.