I could not find any interpretation of the US constitution that US citizens have the right of life and safety. So what is the constitutional base for laws of crimes against the person (murder, battery, rape...)?
Does the provision of the 5th amendment "be deprived of life, liberty, or property, without due process of law" applies also against criminals or it is intended only against government?
You have a couple major misconceptions about US law.
First, crimes against the person are generally punished at the state level. States are not restricted to any sort of enumerated powers, and can pass any law they want to promote the general welfare unless there's a reason they can't. This is called the "general police power," and it lets them make everything from contract law to laws against murder. The federal government has to justify what gives it the authority to pass a law, and cities and counties have to justify their authority with state law or a state constitution, but a state government never has to preemptively justify why they have the authority to pass a law.
States are especially not limited to powers listed in the federal constitution. The US Constitution sets up the federal government. State governments are set up by state constitutions, and derive their authority directly from the consent of the people of the state exercising their right to democratic self-determination. The only powers the US Constitution gives to states are minor technical powers involving state-federal relations (e.g. deciding how their presidential electors are appointed). But as I said, they aren't generally limited to any sort of enumerated powers by their state constitution either.
Even the federal government isn't limited to "protecting rights listed in amendments." That's very little of what it does, in fact. Congress has powers listed (for the most part) in Article I and Article IV. It can pass laws banning murder in DC because Article I lets it exercise exclusive jurisdiction (meaning general police power) over DC and over federal enclaves. Article IV lets it exercise general police power over US territories, and pass laws regarding other federal property (I think it has a general police power there too, at least according to current law). The Necessary and Proper clause gives Congress the power to protect its own operations by, for instance, criminalizing the murder of a federal judge. Etc. Where there isn't a clear thing that lets the feds regulate something, they can probably get away with cramming "in or affecting interstate or foreign commerce" in the law, secure in the knowledge that practically everything affects interstate commerce.
I'm not sure where you got the idea that laws are passed exclusively to enforce rights protected by the Constitution. They are not. They are not passed primarily for that purpose. Such laws do exist (e.g. deprivation of rights under color of law, which was passed pursuant to the 14th Amendment), but they're protecting you from government infringement of that right.
The ability of the government to define and punish crimes does not stem from a right of the citizen.
The US can define and punish crimes because of several enumerated powers in Article 1 Section 8, combined with the Necessary and Proper Clause and an expansive reading of the Commerce Clause.
For example, murder for hire involves commerce. Murder on a ship implicates the enumerated power to "define and punish Piracies and Felonies committed on the high Seas". When a murder involves crossing a state border, it implicates the Commerce Clause (using a channel of interstate commerce).
To clarify how the Commerce Clause can be used to justify the creation of a federal crime, United States v. Lopez 514 U.S. 549 (1995) describes some of the limits on what the Commerce Clause allows federal government to regulate (internal citations removed):
Consistent with this structure, we have identified three broad categories of activity that Congress may regulate under its commerce power. First, Congress may regulate the use of the channels of interstate commerce. (The authority of Congress to keep the channels of interstate commerce free from immoral and injurious uses has been frequently sustained, and is no longer open to question.) Second, Congress is empowered to regulate and protect the instrumentalities of interstate commerce, or persons or things in interstate commerce, even though the threat may come only from intrastate activities. Finally, Congress' commerce authority includes the power to regulate those activities having a substantial relation to interstate commerce i. e., those activities that substantially affect interstate commerce.
