Your last query first...
3) How does upgrading to Fast Ethernet affect the event of collisions?
The collision domain of Fast Ethernet is 1/10th the size of the collision domain in 10-Mbit/sec Ethernet. This is because of the 10-times increase in speed of the network. It also means that Fast Ethernet networks can only be one-tenth the physical size of a 10Base-T network.
Shared Fast Ethernet provides much higher bandwidth and therefore, the possibility of collisions decreases ( this also depends on your network design since only 1 (or 2) hub(s) is legally allowed in a single segment in 100BASE-T networks).
It should be noted that Fast Ethernet supports full-duplex switched mode to provide even better performance than your regular 10Base-T. A full-duplex non-shared link doesn't even need CSMA/CD, because no other stations are trying to use the link, and each end system has its own channel to transmit on. Since there is no chance of a collision therefore, collision detection and loopback functions can be disabled.
2) What effect does adding more tarffic per user on a shared media LAN have on the occurence of collisions?
The bandwidth remains constant, though the throughput will suffer since more frames will be travelling over the same amount of bandwidth and therefore, the likelihood of more collisions.
1) What effect does adding more users to a shared media LAN have on the occurrence of collision?
With shared Ethernet, the likelihood of collision increases as more nodes are added to the shared collision domain of the shared Ethernet.
And you are correct when you say, "The more collisions, the longer the maximum back-off time as back-off time is dependent on the number of consecutive collisions that were issued before a successful transmission. "
I would suggest you to have a look at these,
www.firewall.cx/ethernet-collisions-intro.php
look at the answer for question 2 in the following document,
www.erg.abdn.ac.uk/users/gorry/course/ex...67-04-1-Solution.pdf
and if you're still curious and want more technical detail, go for these,
www-net.cs.umass.edu/cs653-2002/documents/ethernet_552.pdf
www.erg.abdn.ac.uk/users/gorry/course/lan-pages/csma-cd.html
Exponential backoff algorithm has been nicely explained here, (skip the ALOHA part if your not interested)
www.cs.virginia.edu/~jorg/teaching/cs457/slides/lanp1.pdf
