c - Whole one core dedicated to single process
Is there any way in Linux to assign one CPU core to a particular given process and there should not be any other processes or interrupt handlers to be scheduled on this core?

Yes there is. In fact, there are two separate ways to do it :-)
Right now, the best way to accomplish what you want is to do the following:

Add the parameter isolcpus=[cpu_number] to the Linux kernel command line from the boot loader during boot. This will instruct the Linux scheduler not to run any regular tasks on that CPU unless specifically requested using cpu affinity.
Use IRQ affinity to set other CPUs to handle all interrupts so that your isolated CPU will not receive any interrupts.
Use CPU affinity to fix your specific task to the isolated CPU.

This will give you the best that Linux can provide with regard to CPU isolation without out-of-tree and in-development patches.
Your task will still get interrupted from time to time by Linux code, including other tasks - such as the timer tick interrupt and the scheduler code, IPIs from other CPUs and stuff like work queue kernel threads, although the interruption should be quite minimal.
For an (almost) complete list of interruption sources, check out my page at https://github.com/gby/linux/wiki
The alternative method is to use cpusets which is way more elegant and dynamic but suffers from some weaknesses at this point in time (no migration of timers for example) which makes me recommend the old, crude but effective isolcpus parameter.
Note that work is currently being done by the Linux community to address all these issues and more to give even better isolation.
