It depends.
1) Mechanically, it is easy -- in my opinion. You have to disconnect all the cables going to the motherboard. You have to remove all the items attached to the motherboard, such as the CPU and memory. You may have to loosen or remove anything else that is in the way, such as the CD drive, depending on your case design.
The new motherboard should be the same form factor as your old.
When putting the CPU back in, you remove old heat sink compound from both the CPU and heat sink, and put new compound on.
But, there can be other problems. See below.
2) Yes, it is easy to damage the motherboard or other component. A big danger is from electrostatic discharge. A "zap" smaller than you can feel is enough to cause damage. Another danger is breaking a connection because of too much pressure, or careless handling. You can also damage components you remove, such as the CPU.
3) In your case, probably not. But, it depends.
If you want to take out an old technology motherboard and put one of more modern design, you may have trouble finding one that is compatible with your CPU. If you have more than 2 PATA devices, you may have to give some up.
(In case you don't know, PATA drives take a wide parallel, 40 pin IDE cable. PATA has been superseded by SATA. SATA drives have a narrow, 7 pin cable. (Technically, SATA is also IDE.) )
That your machine now has an Core Duo processor indicates that it is a recent model, so the likely hood that you can find one compatible with your CPU, memory and drives is good.
If you change your motherboard, you could have problems with it being compatible with driver installations on your computer, particularly if you have a MS Windows O/S. This could prevent you from booting the computer after swapping the main board. If the computer can be booted, you could have Windows Activation issues. To prevent this, you will need to initiate a process to "upgrade" the O/S before you change the motherboards.
Newegg.com has a feature called "power search" that allows you to select your requirements for a motherboard. It would help if you were to use that, and get a board that is close to the one you have now. Try to get one that has the same or similar chip set, North Bridge and South Bridge.