How is the BIOS ROM mapped into address space on PC?
ROM responds to both regions due to memory aliasing. According to this Dr. Dobbs article written by Pete Dice of Intel:
For legacy option ROMs and BIOS memory ranges, Intel chipsets usually come with memory aliasing capabilities that allow access to memory below 1 MB to be routed to or from DRAM or nonvolatile storage located just under 4 GB. The registers that control this aliasing are typically referred to as Programmable Attribute Maps (PAMs). Manipulation of these registers may be required before, during, and after firmware shadowing. The control over the redirection of memory access varies from chipset to chipset For example, some chipsets allow control over reads and writes, while others allow control over reads only.
Check out the article for more low level details on device memory mapping and memory initialization, configuration, and testing.
On the PC there's always some address decoding logic involved because there are a few "holes/windows" in the physical address space through which the BIOS ROM and I/O devices (e.g. video card) are accessible instead of the RAM. That's by design, for compatibility reasons, so older programs can still run on newer computers.
As for the initial address at which the CPU starts execution after a reset, if you look at the documentation, you will see that Pentium-class CPUs start with this:
EIP=0xFFF0
CS.Selector=0xF000
CS.Base=0xFFFF0000
If you follow the normal real-mode addressing scheme, the physical address should be CS.Selector*16+IP, or, with the values substituted, 0xFFFF0. However, the CPU actually calculates the address using CS.Base+(E)IP (in the real and 16/32-bit protected mode, but not in virtual 8086 or 64-bit protected mode), hence the first address that the CPU requests from the memory is going to be 0xFFFFFFF0. Your inability to use far jumps to code within the ROM at that high address may be due to the fact that loading into CS will reset CS.Base to 16 * the new value of CS.Selector. So, jumping to, say, 0xF000:0xFFF0 will transfer control to 0xFFFF0 instead of 0xFFFFFFF0 and unless the ROM is also mapped at that low location in the memory and the code in it is suited for running with CS(.Selector)=0xF000, it's not going to run.
Also, neither the CPU nor the circuitry around it has to support all 32 (or more) address lines if the PC is limited to have at most 16MB (as it was on i80286 and i80386SX) or 4GB (as it was on i80386DX/original i80386 and i80486) or 240-52 bytes (on 64-bit capable Pentium-class CPUs) and if that's the case, if a number of high bits in the physical address space are ignored, execution can be said to effectively start at an address lower than the theoretical maximum - 16, e.g. 0x00FFFFF0 (i80286/i80386SX).
If you need to resolve problems with your board, see its documentation and schematics to find out how the ROM is mapped into the physical address space on it.