Do I need a party wall surveyor to serve notice or can I serve notice myself?

It is possible for you to serve notices yourself, but it may be wise to hire a party wall surveyor ,such as us,  to do it for you. This is because self-served notices are often invalid, usually due to a lack of understanding of how the Act works.
 

What happens if the person to whom it is addressed does not receive it? 

If you serve it correctly then that is all you can do. It is best if using the postal service to get proof of postage. After 14 days, there will be a deemed dispute if no consent is received in response to the notice. 

How do I know if I have to serve an excavation notice when I do not know how deep  my neighbours foundations are?

If you reside in a semi-detached or terraced house, the foundations of the neighbouring properties are likely to be of similar depth to yours. You can excavate a trial hole on your land to confirm this. However, older properties tend to have shallower foundations; pre-war buildings typically have a foundation depth of 400mm, while post-war buildings have a depth of 600mm. Conversely, modern foundations are usually at least 900mm deep.