In my HFT software I plan to use one core for stock index calculation. That would be simply while(true) loop without any delays which will calculate (sum and multiply) components as often as possible (so millions times per second) and I plan to do that 8 hours per day every day.
I was never before loading my computer to 100% full time every day regullary. May it be dangerous? Do processor has kind of "resource" (very big of course) after which it can stopped working?
There's no danger (when using server-class hardware).
I've run hundreds of HFT systems where we'd designate a CPU core to run a spinlock thread (to reduce interrupts) or have strategies pegged to specific CPU cores for the duration of the trading day. This is what the CPUs were designed for. I can say that I've never had a processor fail in this context.
In your situation, are you using a proper server? Other factors to consider are cooling, redundant fans, power supplies, etc. But those are standard items for any production system.
In general, no, though what you should be looking at is load, but temperatures. You might want to simulate the load (perhaps with superpi on windows, prime95 on linux and windows or some other stress test application, or your actual application) and run the process until the temperature stabilises -similar to what an overclocker would do.
You want this temperature to be under the maximum rated temperature for that processor -look up the datasheet for that. Then see if your cooling solution is adequate and presumably adjust it as needed. I can't suggest monitoring software, unfortunately without knowing an OS - the usual suspects such as nagios may work, but for a initial 'burn in', something like lmsensors or pcwizard may do for a single system.
Most modern processors will simply throttle down if they overheat - intel has a page on this. It would be horrible for your application if performance is critical, but its more likely the system will shut down or act strange rather than burn itself out. Thats a sign the processor is overtaxed, and bad things are happening - review your cooling choices in that case.
Thousands of scientific clusters worldwide consider it a suboptimal (or bad) situation when there are cores that are not at 100% CPU load. Real servers with proper server grade hardware are designed for this.