Why does a receptor molecule undergo a conformation change when its ligand binds to it? (And does this only apply to receptors bound to the cell membrane or can it also occur with receptors in the cytoplasm of a target cell?)
Why? I think the Why answer to that is honestly a bit beyond VCE, especially when they only teach you about enzymes in terms of lock and key. Where did you obtain the question?
If you mean why in different sense (functional), it changes in response to the ligand so that it can open (ion channels, etc)/perform the function activated by the ligand (other types). Think of it as a switch, it turns them "on" to do their function. If they were always on, they'd be kind of useless, so a switch is helpful.
If you mean why in a chemical/structural sense, i think its beyond VCE unless the curriculum has vastly changed.
When Na+ ions enter a neuron to trigger an action potential, do they enter by action transport or facilitated diffusion through the sodium channel?
Inside the cell is low in Na+, outside the cell is high in Na+, what does your knowledge of diffusion tell you about these things?
Na+ cant easily diffuse through the membrane because of its charge but the concentration gradient still exists for it to diffuse. The channel helps this process occur.
Another question relating to signal transduction: I'm not entirely sure what would happen to the receptor molecule and the signal transduction pathway if the signal molecule is broken down?
Depends when it is broken down, there is a proper time for it to be broken down for instance. If it is broken down when it isn't meant to be, the pathway will likely be impacted of course. If it's broken down very early, it'd be like the receptor molecule was never activated.