how does a program runs in memory and the way memory is handled by Operating system
1) What is the stack which this image is referring to?
The stack is for allocating local variables and function call frames (which include things like function parameters, where to return after the function has called, etc.).
2) What is memory mapping segment which is referring to file mappings?
Memory mapping segment holds linked libraries. It also is where mmap calls are allocated. In general, a memory mapped file is simply a region of memory backed by a file.
3) What does the heap have to do with a process. Is the heap only handled in a process or is the heap something maintained by the operating system kernel and then memory space is allocated by malloc (using the heap) when ever a user space application invokes this?
The heap is process specific, and is managed by the process itself, however it must request memory from the OS to begin with (and as needed). You are correct, this is typically where malloc calls are allocated. However, most malloc implementations make use of mmap to request chunks of memory, so there is really less of a distinction between heap and the memory mapping segment. Really, the heap could be considered part of the memory mapped segment.
4) Does this mean that at a time only one program runs in memory occupying entire 4 GB of RAM?
No, that means the amount of addressable memory available to the program is limited to 4 GB of RAM, what is actually contained in memory at any given time is dependent on how the OS allocated physical memory, and is beyond the scope of this question.
5) Is it referring to randomizing the stack within a process or is it referring to something which is left after counting the space of all the processes?
I've never seen anything that suggests 4gb of space "hampers" the effectiveness of memory allocation strategies used by the OS. Additionally, as @Jason notes, the locations of the stack, memory mapped segment, and heap are randomized "to prevent predictable security exploits, or at least make them a lot harder than if every process the OS managed had each portion of the executable in the exact same virtual memory location." To be specific, the OS is randomizing the virtual addresses for the stack, memory mapped region, and heap. On that note, everything the process sees is a virtual address, which is then mapped to a physical address in memory, depending on where the specific page is located. More information about the mapping between virtual and physical addresses can be found here.
This wikipedia article on paging is a good starting point for learning how the OS manages memory between processes, and is a good resource to read up on for answering questions 4 and 5. In short, memory is allocated in pages to processes, and these pages either exist in main memory, or have been "paged out" to the disk. When a memory address is requested by a process, it will move the page from the disk to main memory, replacing another page if needed. There are various page replacement strategies that are used and I refer you to the article to learn more about the advantages and disadvantages of each.