This all depends on the motherboard and the processor type. Rule of thumb...If there is a release of some sort, a lever, a bush tab etc it is removable.
No, a processor is not fixed to the motherboard. Most modern processors are designed to be easily removable and replaceable using a socket on the motherboard. This allows for easy upgrades or replacements without replacing the entire motherboard.
Processor, RAM, daughter cards, CMOS, Heat sink
Depends on what processor you're using. Go to the manufacturer's site and find the product, it should tell you the socket that the processor requires. Any motherboard with that socket will be compatible
Motherboard
Processors don't connect to a motherboard, there are installed in a socket. What determines if a processor is compatible is the type of processor... PGA(AMD most of the time) or LGA(Intel) and the ammount of pins that are on the motherboard/processor.
"845G" is a chipset, not a processor. The chipset is actually a part of the motherboard, and should be advertised in it's specs.
Many motherboards have CPUs and graphics cards (GPUs) that attach to the motherboard via sockets. Some, however, have components that are soldered on to the motherboard and not meant to be removed. ASUS ROG series computers, for example, typically utilize GPUs and CPUs that are attached to the motherboard (they do not attach with a socket). You will notice that Intel CPUs with the "HQ" designation are the chips that are soldered on to the motherboard and are not meant to be removable. Intel CPUs ending in "MQ" are removable and can be easily swapped in and out of motherboards. Examples would be "Intel Core i7-4700HQ Processor" (non-removable) or "Intel Core i7-4810MQ Processor" (removable). Some things that are almost universally attached to the motherboard for all computers would be the PCI express sockets, CPU socket and connections for peripheral devices (like USB and headphone jacks).
If you spot the processor, it should be labeled right on there with a P4 or a PII just check the processor type and this could tell you the difference
function of the processor is to process data
Pci cards
Motherboard
processor