Q1.
Suppose i have a situation where there is an Oracle server and
a number of client stations from which i wish to be able to
administer the server. Does it mean that i have to copy the
parameter file and associated files to all the client
stations?

On the server, in the directory where your DB lives, you need a file called initmydb.ora (mydb being the identifier of you databse ,orcl by default) This holds all of the start up parameters for the database. On any workstation that uses OEM (Oracle Enterprose manager) needs a copy of this as well. With that, you can stop/start oracle services.
From the command line (svrmgr30) you give the command
svrmhr30 > startup pfile=initmydb.ora;

Q2.
What are those "associated files" and should i include them
into the Backup - Restore plan?

In order for a client to see an Oracle table, there must be a tnsnames.ora file.
This holds the connection information, including the alais of the database. The easiest way to maintain this file is with net80 config. It will make the changes and test the connection for you. This is installed with the Oracle client.
For backup, I assume you mean the database, so you need the control files.
The OEM backup Wizard is a good tool to use, if if you vcannot get it work, it creates the script for backing up an Oracle database. If you mean a full OS backup, get the whole directoy(ies) where your data resides.