My 2 cents:
Question 1- The illustration market (As I know it living in the U.S.)
is flooded, but there's always room for talented artists- and the jobs go to
the ones that have good communication skills and deliver the work on time
You probably won't get an agent to start- mostly because they want
to have a published artist that can get them jobs as well. Of course
that is an educated guess at best. I would get a directory, send a few emails,
press packets or talk to few agents personally to find out. Some agencys deal in
a specific type of art/ medium, and they all have their own set of conditions
unique to the agency.... so research is important.
Question 2- PDF and JPGs are fine for sending by email.
I usually zip the final TIFF and upload it to my server for easy download
for the client.
Question 3- You can have them sign and scan the contract
or mail it to you. If you have a kill fee, or seperate fees for the sketch/concept
stages it will save you some trouble if they drop the job for their reasons-
and you will be paid for the work thus completed.
Question 4- Sample Contracts/ Invoices and Business Practices
for the Graphic Arts Field
I know you want to listen to your teacher...but seriously.
He/she is one person w/ one opinion. If you want to be an illustrator, be an illustrator.
In fact...there you are "You are an illustrator" congratulations.
Now to get your work published- think locally. You want to do fashion illustration?
Do some drawings for a local fashion show poster/program.Go to the local theater and meet with the costume designer and see if you can help out with some drawings- just be enthusiastic
Lastly-make a move- try it out...don't give up something before you try it.
If it really is the thing for you, make an effort
good luck to you