1. How many is too many? Is there a limit being preset or set by us on the number of active/dead connection on an Oracle server?

--I'm not sure here and you are referring INACTIVE session as Dead connection. As such there is no dead connection unless you kill it, it becomes Pseudo session.

--Too many is as many you defined in the no of processes in init.ora (if its dedicated mode, if not based on your MTS config)

2. How to view the number of active/dead connections on an Oracle server? Is there a tool we can use?

--Check V$session view for status colum to figure out the session status

3. I am thinking to resolve their problem in this way:
a) add resource_limit = true to init.ora file on the server
b) create a profile with idle_time set inside.
c) assign the profile to the db user.

is this approach sounds fine to you?

--Totally Depend on the way your application works. No clue how your application works. Think about SQLNET_EXPIRE_TIME parm also. Search metalink for Deac connection detection on this parm usage, there are some limitations which stopped me to take advantage of the this parm.