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Additional answers to your questions.
a) How many IP networks are in the diagram and what are they?
Two, 192.160.10.0/24 and 172.16.0.0/16.
b) If PC0 wishes to ping PC1, how can it determine that PC1 is on the same network?
PC0 can compare PC1's IP address against its IP address and network mask. This will tell it if the destination IP is in the same subnet.
c) If PC0 wishes to ping PC1, and PC0 doesn't know PC1’s MAC address what will it do?
PC0 will ARP for PC1's MAC.
d) Does any problem occur in the network if PC0 and PC1 send frames simultaneously? Explain your answer.
Mostly depends on whether the two hosts support full duplex and/or whether they have the same bandwidth. If not full duplex, transmitting frames can collide with received frames. If different bandwidths, the faster might congest on the switch port to the slower.
Even if full duplex and same speed, not all host NICs (or even some switches) can handle full capacity. I.e. it's possible a host or the switch might not be able to support full duplex at full wire-speed/line-rate. If both hosts send frames simultaneously, there may be more "work" for host and/or switch interfaces.
e) What information will the Finance Switch have about PC0 and PC1 after they have sent frames?
PC0's and PC1's MAC associated with the port they are connected to.
f) What information will the Finance Office router contain to allow it to make routing decisions?
A routing table contain network destination. The router will implicitly know of directly connected networks. For non-directly connected networks, like what's on the far side of Sales Office Router, it will need to have such routes defined to its routing table.
