(Nodal) Processing Delay
The (nodal) processing delay is every device along the communication path that actually processes/examines the packets; these include routers, switches, and statistical multiplexers. The receiver doesn’t count towards this delay because the receiver is the receiver and has received the packet at that point, it doesn’t matter what will be done on its side with the signal.
Regarding proxies and VPNs: yes, every device that does anything with the packets counts towards the delays. Especially NATs (rewriting) or devices that perform deep packet inspection add a lot of processing time.
nodal processing = node processing
nodal processing ≠ nodal delay
(Total) Nodal Delay
The (total) nodal delay on the other hand is the sum of all latency delays. There are exactly four delays:
- (Nodal) Processing Delay amount of time used to process the packet headers, check for bit errors and determine the destination host.
- Queuing Delay amount of time a packet is waiting in the queue (buffer) before it can be pushed on the link.
- Transmission Delay amount of time necessary to push all the bits on the link.
- Propagation Delay amount of time it takes the signal’s header to travel from the sender to the receiver.
dnodal = dproc + dqueue + dtrans + dprop
According to Table 1 in this paper typical timings for each delays are:
- dproc = 10–1,000 µs
- dqueue = 0…∞
- dtrans = 10 µs
- dprop = 1,000 µs
The queue delay may reach infinity and the whole network suffers from congestion collapse; which actually happened during the 1980s and was the reason why Congestion Avoidance and Control was invented.
As a packet travels from one node (host or router) to the subsequent node (host or router) along this path, the packet suffers from several types of delays at each node along the path. The most important of these delays are the nodal processing delay, queuing delay, transmission delay, and propagation delay; together, these delays accumulate to give a total nodal delay.
— (Kurose and Ross 2013, 35–36)
This is only a very terse primer on the subject, I encourage you to read on.
 Of course it matters, but it doesn’t matter for the delay calculations because we are only interested in the delay incurred by the underlying network and not the delays within sender and receiver.
 I’ve seen that the receiver is sometimes counted as well. I don’t know if this is correct or not, a good reference is needed here.
 This number is much higher in real world and highly depends on the distance to cover, also the last mile problem is very important here.