Are C keywords/functions not enclosed in std namespace in C++?
Keywords (and also macros): No, those are not in namespaces.
Functions, types and variables (i.e. all identifiers except macros): Depends on which standard header you include.
If you include C standard header such as <stdint.h>, then the names will be in the global namespace. They may also be in the std namespace, but that is not guaranteed.
If you include the corresponding <cstdint> header, then the names from the C standard header are guaranteed to be in the std namespace. They may also be in the global namespace, but that is not guaranteed.
You've failed to include either <stdint.h> or <cstdint>, so there is no guarantee that int32_t would be declared in either namespace. But you've included another standard header and therefore there is no guarantee that it wouldn't be declared in some namespace - because standard headers may include other headers; you should never rely on such transitive inclusion (in the way that your example relies on it) unless documented in the standard.
Same applies to the time function. You've included a standard header and there is no guarantee that it wouldn't include another standard header which declares time. And there is no guarantee that it wouldn't be in the global namespace.
Regardless of whether you include any standard headers, all names used by the C standard library are reserved to the language implementation in the global namespace. By defining ::time yourself, the behaviour of your program will be undefined (UB is allowed to fail compilation, which is the best outcome).
Can I be assured that there would be no problem with the name clashing if I declare variables in local space?
In case of time, Yes. C standard names (except macros of course) are reserved only in the global namespace. Local names are not in the global namespace; they will shadow the global one, which is fine. It is also fine to define these in your own custom namespace.
Macro names, as well as certain identifiers such as those that include double underscore are reserved in all namespaces. All macro names are all upper case, so it is easy to avoid them by including lower case characters in names.
To avoid name conflicts with standard names, as well as third party libraries, one should only declare one name in the global namespace (besides main): A (hopefully unique) namespace that contains all other namespace scope declarations. And macros should be avoided when possible, but where necessary, they should include some (hopefully unique) prefix.